Coordinate Geometry Mathematic

Coordinate Geometry Mathematic 

Coordinate Geometry Mathematic 

Important information:- It is a system of geometry, where the position of points on the plane is described by using an ordered pair of numbers. 

#Rectangular Coordinate Axes :- The lines XOX' and YOY' are mutually perpendicular to each other and they meet at point O which is called the origin. 

Quadrants:- The X and Y-axes divide the cartesian plane into four regions referred to quadrants

Table of Contain:-   

#On which axis does the point (6, 0) lie?

#The intersection point on the x-axis of 7x - 3y = 2 is  ?

#If the points A 1,-1 B 5, 2 and C k &,5 are collinear, then k = ? 

# If two vertices of a triangle are (5, 4) and (-2, 4) and centroid is (5, 6), then third vertex is

#Find the equation of the line which makes equal intercepts on the axis and passes through the        point (4, 5). 

 1. In which quadrant, does the point (- 5, 7) lie? [Railways 2004] 

     (a) 1st 

     (b) 2nd

    (c) 3rd 

    (d) 4th

  Answer :- (b) 2nd

 2. On which axis does the point (6, 0) lie?

     (a) x-axis

     (b) y-axis

     (c) Either x or y

     (d) At origin 

     (e) None of the above 

Answer :- (a) x-axis

3. The distance of the point P (8, - 6) from the origin is 

    (a) 2 units

    (b) 8 units

    (c) 10 units

    (d) 16 units

    (e) None of the above

Answer :- (c) 10 units

 4. If the distance between the points (x, 0) and (-7, 0) be 10 units, then the possible values of x             are   ?

    (a) 3 and 17

    (b)-3 and 17 

    (c) 3 and -17

    (d) -3 and -17

Answer :- (c) 3 and -17

 5. If the distance of the point P (x, y) from A(a, 0) is a + x, then y 2 = ? 

    (a) 2ax

    (b) 4ax 

    (c) 6ax 

    (d) 8ax 

    (e) None of the above

Answer :-   (b) 4ax 

 6. The intersection point on the x-axis of 7x - 3y = 2 is  ?

     (a)  2/5

     (b) 2/7

     (c) 3/4

     (d) 3/7

  Answer :- (b) 2/7

7. Locus of the points equidistant from the points (- 1,-1) and (4, 2) is

   (a) 5x - 3y - 9 = 0

   (b) 5x + 3y + 9 = 0 

   (c) 5x + 3y - 9 = 0

   (d) 5x - 3y + 9 = 0

   (e) None of the above

Answer :- (c) 5x + 3y - 9 = 0

 8. Coordinates of a point is (0, 1) and ordinate of an another point is - 3. If distance between both       the points is 5, then abscissa of second point is

     (a) 3 

     (b) -3

     (c) ±3 

     (d) 1

     (e) -1 9. 

Answer :-  (c) ±3 

9. The vertices of a triangle are A (4, 4), B 3,- 2 and C (- 3,16). The area of the triangle is 

    (a) 30 sq units 

    (b) 36 sq units

    (c) 27 sq units 

    (d) 40 sq units 

    (e) None of the above 

Answer :-  (c) 27 sq units 

10. Two vertices of an equilateral triangle are origin and (4, 0). What is the area of the triangle?

      (a) 4 sq units 

       (b)  3 sq units

       (c) 4✓3 sq units 

       (d) 2✓3 sq units 

       (e)  5✓3 sq units 

Answer :-  (c) 4✓3 sq units 

11. If the points A 1,-1 B 5, 2 and C k &,5 are collinear, then k = ? 

     (a) 2

     (b) 4

     (c) 6 

     (d) 9 

     (e) None of the above 

Answer :-   (d) 9 

12. Slope of x-axis is 

     (a) 0

     (b) 1

     (c) -1

     (d) ~ 

     (e) None of the above 

Answer :- (a) 0

13. Slope of y-axis is 

      (a) 0 

      (b) 1 

      (c) -1 

      (d) ~

      (e) None of the above 

Answer :-  (d) ~

14. If two vertices of a triangle are (5, 4) and (-2, 4) and centroid is (5, 6), then third vertex is

      (a) (12,10)

      (b) (10,12) 

      (c) (-10,12) 

      (d) (12,-10)

      (e) (-10,-12) 

Answer :- (a) (12,10)

 15. The points (2, 2) (6, 3) and (4, 11) are the vertices of

       (a) an equilateral 

       (b) a right angled triangle 

       (c) an isosceles triangle 

       (d) a scalene triangle

       (e) do not form triangle 

Answer :- (b) a right angled triangle 

16. A point C divides the line AC, where A(l, 3) and B (2, 7) in the ratio of 3 : 4. The coordinates           of    C are   ?

     (a)  (5/3 , 5)

     (b) (3/5 , 5)

     (c) (-2 , -9)

     (d) (10/7 , 33/7)

 Answer :-  (d) (10/7 , 33/7)

17. The slope of a line passing through the points A (4, - 3) and B (6, - 3) is 

      (a) 4

     (b) 0

     (c) -

     (d) 5

     (e) None of the above 

Answer :- (b) 0

18. If the inclination of a line joining the points A (x, - 3) and B (2, 5) is 135°, then z=?

     (a) 10 

     (b) 15

     (c) 20 

     (d) 25 

     (e) None of the above 

Answer :-  (a) 10 

19. If a point (x, y) in a OXY-plane is equidistant from (-1,1) and (4, 3), then [CLAT2013] ?

      (a) 10x + 4y = 23 

      (b) 6x + 4y = 23

      (c) -x +y = 7 

      (d) 4x+3y=0 

Answer :- (a) 10x + 4y = 23 

20. If the graph of the equation 2x+ 3y = 6 form a triangle with coordinates axis, then the area of          triangle will be [SSC (10+2) 2012]

      (a) 2 sq units 

      (b) 3 sq units

      (c) 6 sq units

      (d) 1 sq units

Answer :-  (b) 3 sq units

 21. If A -5, 7) B -4,-5) C-1,-6) and Z) (4,5) are the vertices of a quadrilateral, then find the area of         the quadrilateral ABCD.

        (a) 72 sq units 

        (b) 80 sq units 

        (c) 90 sq units

        (d) 92 sq units 

        (e) None of the above 

Answer :- (a) 72 sq units 

22. Find the equation of a line parallel to y-axis and passing through the point (- 3, 4) 

       (a) x + 3 = 0 

       (b) x - 3 = 0 

       (c) x + 4 = 0 

       (d) x - 4 = 0

       (e) None of the above

Answer :- (a) x + 3 = 0 

 23. Find the equation of a line of unit slope and passing through the origin. 

        (a)  y = x

        (b) x + y = 0

        (c) x = y + 1

        (d) x = 1/2y +1

Answer :- (a)  y = x

24. The value of k for which the lines x + 1y = 9 and kx + 4y = - 5 are parallel, is

       (a) k = 2 

       (b) k = 1 

       (c) k = - 1

       (d) k = 3 

       (e) None of the above 

Answer :- (a) k = 2 

25. Find the value of k for which the lines 5x + 3y + 2 = 0 and 3x - ky + 6 = 0 are perpendicular. 

     (a) 5 

     (b) 4 

     (c) 3 

     (d) 2

     (e) 1 

Answer :-  (a) 5 

26. The length of the equation 4x+ 3y - 12 = 0 that intersects two coordinate axes is

       (a) 2.5 units 

        (b) 7 units 

        (c) 5 units

         (d) 6 units

Answer :- (c) 5 units

 27. Find the distance of the intercept at point of x-axis and the line 5x+ 9y - 45 from origin. 

       (a) 5

       (b) 9

        (c) 5/9

        (d) 9/5

        (e) None of the above 

Answer :-  (b) 9

28. Find the equation of perpendicular bisector of the line made by joining the points (1, 1)

       and (3, 5). 

      (a) x + 2y + 8 = 0 

      (b) x - 2y + 8 = 0

      (c) x - 2y - 8 = 0

      (d) x + 2y - 8 = 0 

      (e) None of the above 

Answer :- (d) x + 2y - 8 = 0 

29. Find the equation of the line which makes equal intercepts on the axis and passes through the        point (4, 5). 

      (a) x+ y = 9

      (b) x+2y = 7 

      (c) 2x+2y = 7 

      (d) 2x + y = 7 

Answer :- (a) x+ y = 9

30. In what ratio, the line made by joining the points A (- 4,- 3) and B (5,2) intersects x-axis?

     (a) 3 : 2 

     (b) 2 : 3 

     (c) -3 : 2

     (d) -2:3

     (e) None of the above 

Answer :- (a) 3 : 2 

31. Find the ratio in which the line 3x + y - 9 divides the line made by joining the points (1, 3) and        (2, 7).

      (a) 3:4 external 

      (b) 3:4 internal 

      (c) 1 : 4 internal 

      (d) 4:3 internal 

      (e) None of the above 

Answer :- (b) 3:4 internal 

32. If the point (x, y) is equidistant from points (7, 1) and (3, 5), find (x - y).

      (a) 2 

      (b) 4

      (c) 6

      (d) 8

      (e) None of the above 

Answer :- (a) 2 

33. The area of the region bounded by y =  |x| - 5 with the coordinate axis is [SSCCGL2012] 

      (a) 25 sq units

      (b) 52 sq units

      (c) 50 sq units

      (d) 20 sq units 

Answer :- (a) 25 sq units

34. If three vertices of a parallelogram are A (3,5) £(-5,-4) and C(7, 10), then fourth vertex is

      (a) (10,19) 

      (b) (15,10)

      (c) (19,10)

      (d) (10,15)

      (e) (15,19)

Answer :- (e) (15,19)

 35. Three vertices of a rhombus are (2,-1), (3, 4) and (-2, 3). Find the fourth vertex.

       (a) (1,2)

       (b) (3,2)

       (c) (-2,-3)

       (d) (-3,-2)

       (e) (2,3) 

Answer :- (d) (-3,-2)

36. Do the points (4, 3), (- 4,- 6) and (7, 9) form a triangle ? If yes, then find the longest side of the        triangle. 

     (a) 18.6

     (b) 16.5

     (c) 24 

     (d) 34

     (e) Triangle can't be formed 

Answer :-  (a) 18.6

37. Are the points (1, 7), (4, 2), (- 1,- 1) and (- 4, 4) vertices of a square? If yes, what is the length          of  the side of square?

      (a) 34

      (b) √34

      (c) 25 

      (d) √25

      (e) None of the above

Answer :- (b) √34

 38. If the points A (6, 1), B(8, 2), C(9, 4) and D(P,3) are the vertices of a parallelogram, taken in             order, find the value of P.

       (a) 3

       (b) 4

       (c) 5

       (d) 6 

       (e) 7

Answer :- (e) 7

Volume and Surface Area Mathematic 2

 Volume and Surface Area Mathematic 2

Volume and Surface Area Mathematic 2

 Important information:- Volume and surface area are related to solids or hollow bodies. These bodies occupy space and have usually three dimensions length, breadth and height.

 #Volume:-  Space occupied by an object is called the 'volume' of that particular object. It is always measured in cube unit like cubic meter, cubic centimeter  etc.

#Surface Area:- Surface area of a solid body is the area of all of its surfaces together. Surface area is measured in square unit like square centimeter , square meter etc.

#Cube:- A solid body having 6 equal faces with equal length, breadth and height is called a cube. In fact, each face of a cube is a square.

#Cuboid:- A rectangular solid body having 6 rectangular faces is called a cuboid

#Room:- A rectangular room has 4 walls (surfaces) and opposite walls have equal areas.

#Box:-  A box has its shape like cube or cuboid. The amount that a box can hold or contain, is called the capacity of the box. Infact , capacity is the internal volume

#Cylinder:- A cylinder is a solid or hollow body that is formed by keeping circles of equal radii one on another. Apart from this, a cylinder is formed by rolling a rectangular sheet also. A cylinder has three surfaces  .

#Cone:- Cone is a solid or hollow body with a round base and pointed top. It is formed by the rotation of a triangle along any of the side

#Frustum:- of Cone If a cone is cut by a plane parallel to the base so as to divide the cone into two parts upper part and lower part, then the lower part is called frustum.

#Sphere:- A sphere is a three-dimensional solid figure, which is made up of all points in the space, which lie at a constant distance from a fixed point. That constant distance and fixed point are respectively called the radius and center of the sphere. In fact, a sphere is like a solid ball.

#Hollow Sphere or Spherical Shell:- Its both external and internal surfaces are spherical and both the surfaces have a common central point.

#Prism:- A right prism is a solid whose top and bottom faces are parallel to each other and are identical polygons that are parallel. The faces joining the top and bottom faces are rectangles and are called lateral faces. The distance between the base and the top is called height or length of the right prism.

#Pyramid :- A solid whose base is a polygon and whose faces are triangles, is called a pyramid. The triangular faces meet at a common point called vertex, "A pyramid whose base is regular polygon and the foot of the perpendicular from the vertex of the base, coincides with the centre of the base, is called a right pyramid."

Table of Contain:-   

# Find the total surface area of a pyramid having a slant height of 8 cm and a base which is a             square of side 4 cm (in cm )

#The base of a cone and a cylinder have the same radius 6 cm. They have also the same height          8 cm. The ratio of the curved surfaces of the cylinder to that of the cone is ?

#What is the volume of the largest sphere that can be curved out of a cube of edge 3 cm? 

#A sphere of radius r has the same volume as that of a cone with a circular base of radius r.               Find the height of the cone. 

 Prism and Pyramid 

77. K prism has the base a right angled triangle whose sides adjacent to the right angle are 10 cm        and 12 cm long. The height of the prism is 20 cm. The density of the material of the prism is 6        g/cu cm. The weight of the prism is ?

     (a) 34 kg

    (b) 48 kg 

    (c) 64 kg 

    (d) 72 kg 

Answer:- (d) 72 kg 

78. A prism and a pyramid have the same base and the same height. Find the ratio of the volumes       of the prism and the pyramid.

     (a) 1:1

     (b) 1: 3

     (c) 3 :1 

     (d) Cannot be determined 

Answer:- (c) 3 :1 

79. The perimeter of the triangular base of a right prism is 60 cm and the sides of the base are in         the ratio 5 : 12 : 13. Then, its volume will be (height of the prism being 50 cm)

     (a) 6000 cm3 

     (b) 6600 cm3

     (c) 5400 cm3

    (d) 9600 cm3

Answer:-  (a) 6000 cm3 

 80. Find the total surface area of a pyramid having a slant height of 8 cm and a base which is a             square of side 4 cm (in cm )

       (a) 80

       (b) 64

       (c) 72 

       (d) 84 

Answer:-  (a) 80

Miscellaneous

81. A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common            radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 

      12.8 cm. The volume V of the structure lies between 

     (a) 370 cm3 and 380 cm3 

     (b) 380 cm3 and 390 cm3

     (c) 390 cm3 and 400 cm3  

     (d) None of the above

Answer:- (a) 370 cm3 and 380 cm3

82. The base of a cone and a cylinder have the same radius 6 cm. They have also the same height          8 cm. The ratio of the curved surfaces of the cylinder to that of the cone is ?

      (a) 4 : 3 

      (b) 5 : 3

     (c) 8 : 5

     (d) 8 : 3 

Answer:- (c) 8 : 5

83. A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of          height 1 cm and base radius 1 mm. The number of cones is ?

      (a) 7500 

      (b) 13500

      (c) 3500 

      (d) 4500 

Answer:- (b) 13500

84. How many spherical bullets can be made out of a solid cube whose edge measures 44 cm, each        bullet being 4 cm in diameter? 

     (a) 2550

    (b) 2541

    (c) 2500 

    (d) 2575 

Answer:- (b) 2541

85. A solid consists of circular cylinder with exact fitting right circular cone placed on the top.              The  height of the cone is h. If total volume of the solid is three times the volume of the cone,          then the height of the circular cylinder is ?

      (a) 3h 

      (b) 3/2 h

      (c) 4h

      (d) 2/3h

Answer:- (d) 2/3h

86. The volumes of a sphere and a right circular cylinder having the same radius are equal. The          ratio of the diameter of the sphere to the height of the cylinder is ?

      (a) 1 : 2 

      (b) 2 : 1

      (c) 2 : 3

      (d) 3 : 2 

Answer:- (d) 3 : 2 

87. Water flows at the rate of 10 m/min from a cylindrical pipe 5 mm in diameter. How long will          it  take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm? 

     (a) 51 min 12 s

    (b) 52 min 1 s

    (c) 48 min 15 s

    (d) 55 min 

Answer:- (a) 51 min 12 s

88. A cylindrical jar, whose base has a radius of 15 cm, is filled with water upto a height of 20 cm.       A solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in              water. Find the increase in the level of water (in cm). 

    (a)  152/27

    (b) 40/7

    (c)  53/9

   (d) 160/27

Answer:- (d) 160/27

 89. A sphere of radius r has the same volume as that of a cone with a circular base of radius r.               Find the height of the cone. 

       (a)  2r

       (b)  r/3

       (c)   4r

       (d)  2/3 r

Answer:- (c)   4r

 90. The radii of a sphere and a right circular cylinder are equal and their curved surface areas             are also equal. The ratio of their volumes is 

       (a) 3 : 4

       (b) 2 : 3 

       (c) 3 : 2 

       (d) 4 : 3 

Answer:-  (b) 2 : 3 

91. The volume of a cuboid is twice the volume of a cube. If the dimensions of the cuboid are 9              cm,   8 cm and 6 cm, then total surface area of the cube will be 

      (a) 213 sq cm

      (b) 216 sq cm

      (c) 218 sq cm 

      (d) 219 sq cm 

      (e) None of the above

Answer:-  (b) 216 sq cm

 92. Let A be a pyramid on a square base and B be a cube. It o, 6 and c denote the number of                edges, number of faces and number of corners, respectively. Then, the result a = b + c is true          for ?

      (a) only A 

      (b) only B 

      (c) both A and B

      (d)  Neither true for  B nor for the A

Answer:- (d) Neither true for  B nor for the A

93. The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at           the rate of  10 per sq m is 15000, then find the height of the hall. 

         (a) 8 m 

         (b) 6 m 

         (c) 9 m 

         (d) 7 m

         (e) None of the above 

Answer:- (b) 6 m 

 94. Seven equal cubes each of side 5 cm are joined end-to-end. Find the surface area of the                   resulting cuboid. 

       (a) 750 sq cm 

       (b) 1500 sq cm

       (c) 2250 sq cm 

       (d) 700 sq cm

       (e) None of the above 

Answer:- (a) 750 sq cm 

95. A hemispherical basin of 150 cm diameter holds water 120 times as much as a cylindrical                tube.  If the height of the tube is 15 cm, then the diameter of the tube is 

      (a) 27 cm

      (b) 24 cm 

      (c) 25 cm

      (d) 26 cm 

Answer:- (c) 25 cm

96. A well of inner diameter 14 m is dug to a depth of 15 m. Earth taken out of it has been evenly         spread all around it to a width of 7 m to form an embankment. Find The height of                           embankment so formed.  

     (a) 7 m 

     (b) 5 m

     (c) 14 m 

     (d) None 

Answer:- (b) 5 m

97. In a shower, 10 cm of rain falls. What will be the volume of water that falls on 1 hector area of        ground? 

      (a) 500 cm3 

      (b) 650 cm3

      (c) 1000 cm3 

      (d) 750 cm3 

Answer:- (c) 1000 cm3 

 98. A large solid metallic cylinder whose radius and height are equal to each other is to be melted        and 48 identical solid balls are to be recast from the liquid metal so formed. What is the ratio          of the radius of a ball to the radius of the cylinder? 

      (a) 1 : 16 

      (b) 1 : 12 

      (c) 1 : 8 

     (d) 1 : 4 

Answer:- (d) 1 : 4 

99. What is the volume of the largest sphere that can be curved out of a cube of edge 3 cm? 

      (a) 9 兀 cm3 

      (b) 6 兀 cm3 

      (c) 4.5兀 cm3

      (d) 3.7 兀 cm3 

Answer:- (c) 4.5兀 cm3

100.A right circular metal cone (solid) is 8 cm high and the radius is 2 cm. It is melted and recast           into a sphere. What is the radius of the sphere? 

       (a) 2 cm

       (b) 3 cm

       (c) 4 cm 

       (d) 5 cm 

Answer:- (a) 2 cm

101. Let the largest possible right circular cone and largest possible sphere be fitted into two                  cubes of same length. Let C and S denote the volume of cone and volume of sphere                          respectively, then which one of the following is correct?  

        (a) C = 2S

        (b) S= 2C 

        (c) S = C 

        (d) C = 3S 

Answer:- (b) S= 2C 

102. 10 circular plates each of thickness 3 cm, each are placed one above the other and a                          hemisphere of radius 6 cm is placed on the top just to cover the cylindrical solid. What is the          volume of the solid so formed? 

       (a) 2647 兀cm3 

       (b) 2527 兀cm3

       (c) 1224 兀cm3

       (d) None of these 

Answer:- (c) 1224 兀cm3

103. A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the           top most ball touches the upper cover of the box, then volume of the empty space in the box is 

       (a) 2500/3 兀 cm3

       (b) 2500兀 cm3

       (c)  5000/3兀 cm3

       (d)  5000 兀cm3

Answer:- (a) 2500/3 兀 cm3

 104. A cone has height which is half of 16.8 cm, while diameter of its base is 4.2 cm. It is melted              and recast into a sphere. Find the surface area of the sphere. 

        (a) 55.4 sq cm 

        (b) 7.8 sq cm 

        (c) 65.58 sq cm 

        (d) 59 sq cm 

        (e) None of the above

Answer:- (b) 7.8 sq cm

  105. A hospital room is to accommodate 56 patients. It should be done in such a way that every             patient gets 22 m of floor and 8.8 m of space. If the length of the room is 14 m, then breadth           and height of the room are respectively 

        (a) 8.8 m, 4 m

        (b) 8.4 m, 4.2 m

        (c) 8 m, 4 m

        (d) 7.8 m, 4.2 m 

Answer:- (a) 8.8 m, 4 m

106. Water flows into a tank 100 m x 150 m x 2 m through a rectangular pipe 1.5 m x 1.25 m at a             speed of 20 km/h. In what time, will the water rise by 2 m? 

         (a) 96 min 

         (b) 50 min 

         (c) 48 min 

         (d) 75 min

         (e) None of the above

Answer:- (c) 48 min 

 107. What part of a ditch 48 m long, 16.5 m broad and 4 m deep can be filled by the earth got by            digging a cylindrical tunnel of diameter 4 m and length 56 m? 

          (a)  1/9

          (b) 7/9

          (c) 8/9

          (d) 2/9

Answer:- (d) 2/9

 108.  Find the area of the iron sheet required দোto prepare a cone double the height of 12 cm                  with diameter of the base 14 cm. 

          (a) 504 sq cm 

          (b) 804 sq cm 

          (c) 304 sq cm 

          (d) 704 sq cm

          (e) None of the above 

Answer:- (d) 704 sq cm

109. A copper sphere of diameter 36 cm is drawn into a wire of diameter 4 mm. Find the length of          the wire. 

        (a) 2000 m 

        (b) 1500 m 

        (c) 1855 m

        (d) 1944 m

        (e) None of the above

Answer:-  (d) 1944 m

Volume and Surface Area Mathematic 1

Volume and Surface Area Mathematic 1

Volume and Surface Area Mathematic 1

 Important information:- Volume and surface area are related to solids or hollow bodies. These bodies occupy space and have usually three dimensions length, breadth and height.

 #Volume:-  Space occupied by an object is called the 'volume' of that particular object. It is always measured in cube unit like cubic meter, cubic centimeter  etc.

#Surface Area:- Surface area of a solid body is the area of all of its surfaces together. Surface area is measured in square unit like square centimeter , square meter etc.

#Cube:- A solid body having 6 equal faces with equal length, breadth and height is called a cube. Infact, each face of a cube is a square.

#Cuboid:- A rectangular solid body having 6 rectangular faces is called a cuboid

#Room:- A rectangular room has 4 walls (surfaces) and opposite walls have equal areas.

#Box:-  A box has its shape like cube or cuboid. The amount that a box can hold or contain, is called the capacity of the box. Infact , capacity is the internal volume

#Cylinder:- A cylinder is a solid or hollow body that is formed by keeping circles of equal radii one on another. Apart from this, a cylinder is formed by rolling a rectangular sheet also. A cylinder has three surfaces  .

#Cone:- Cone is a solid or hollow body with a round base and pointed top. It is formed by the rotation of a triangle along any of the side

#Frustum:- of Cone If a cone is cut by a plane parallel to the base so as to divide the cone into two parts upper part and lower part, then the lower part is called frustum.

#Sphere:- A sphere is a three-dimensional solid figure, which is made up of all points in the space, which lie at a constant distance from a fixed point. That constant distance and fixed point are respectively called the radius and center of the sphere. In fact, a sphere is like a solid ball.

#Hollow Sphere or Spherical Shell:- Its both external and internal surfaces are spherical and both the surfaces have a common central point.

Table of Contain:-   

#The ratio of the radius and height of a 2 ^ cone is 5 : 12. Its volume is 314— cm . Its 7 slant            height is ?

#The diameter of base of a right circular cone is 7 cm and slant height is 10 cm, then what is its          lateral surface area ?

#If the volume of a right circular cone of height 9 cm is 48 7t cm , then find the diameter of its          base.

#If the height of the right circular cone is increased by 200% and the radius of the base is                  reduced by 50%, then the volume of the cone ?

#Weight of a solid metallic sphere of radius 4 cm is 4 kg. The weight of a hollow sphere made             with same metal, whose outer diameter is 16 cm and inner diameter is 12 cm, is ?

Cone and Frustum of Cone

37. The curved surface area of a right circular cone of radius 14 cm is 440 sq cm. What is the                slant  height of the cone?

       (a) 10 cm 

       (b) 11cm

       (c) 12 cm

       (d) 13 cm

Answer:- (a) 10 cm 

38. The diameter of base of a right circular cone is 7 cm and slant height is 10 cm, then what is its          lateral surface area ?

      (a) 110 sq cm

      (b) 100 sq cm

      (c) 70 sq cm 

      (d) 49 sq cm

Answer:- (a) 110 sq cm

39. What is the whole surface area of a cone of base radius 7 cm and height 24 cm?

      (a) 654 sq cm 

      (b) 704 sq cm

      (c) 724 sq cm

      (d) 964 sq cm

Answer:- (b) 704 sq cm

40. What is the volume of a cone having a base of radius 10 cm and height 21 cm?

      (a) 2200 cm3

      (b) 3000 cm3

      (c) 5600 cm3

      (d) 6600 cm3

Answer:- (a) 2200 cm3

41. The diameter of the base of a cone is 6 cm and altitude is 4 cm. What is the approximate                  curved surface area of the cone?

      (a) 45 cm2

      (b) 47 cm2

      (c) 49 cm2

      (d) 51 cm2

Answer:- (b) 47 cm2

42. The volume of a right circular cone is 100 n cm and its height is 12 cm. Find its slant height. 

      (a) 13 cm

      (b) 16 cm

      (c) 9 cm 

      (d) 26 cm

      (e) None of the above

Answer:- (a) 13 cm

43. If the volume of a right circular cone of height 9 cm is 48 7t cm , then find the diameter of its          base.

     (a) 8 cm 

     (b) 4 cm

     (c) 7 cm 

     (d) 11 cm

     (e) None of the above

Answer:- (a) 8 cm 

44. Shantanu's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm.            Find the area of the sheet required to make 5 such caps.

      (a) 5000 sq cm

      (b) 2750 sq cm 

      (c) 3000 sq cm 

      (d) 2700 sq cm

      (e) None of the above

Answer:- (a) 5000 sq cm

45. The radius of the base of a right circular cone is doubled. To keep the volume fixed, the height         of the cone will be?

     (a) Half of the previous height

     (b) One third  of the previous height

     (c) One fourth  of the previous height

     (d) 1/2 times of the previous height

Answer:-  (c) One fourth  of the previous height

46. The radius of the base of a right circular cone is increased by 15% keeping the height fixed.

      The volume of the cone will be increased by ?

     (a) 30%

     (b) 31% 

     (c) 32.25%

     (d) 34.75%

Answer:-     (c) 32.25%

47. The frustum of a right circular cone has the diameters of base 10 cm, of top 6 cm and a height         of 5  cm.  Find its slant height.

        (a) √ 29 cm 

        (b) 3√ 3 cm

        (c) √ 13 cm

        (d) 4√ 3 cm

        (e) None of the above

Answer:-      (a) √ 29 cm 

48. The frustum of a right circular cone has the radii of base 4 cm, of the top 2 cm and a height of        6 cm.  Find the volume of the frustum.

      (a) 115 cm3

      (b) 156 cm3

      (c) 185 cm3

      (d) 176 cm3

      (e) None of the above

Answer:- (d) 176 cm3

49. A cone of radius r cm and height h cm is divided into two parts by drawing a plane through            the middle point of its height and parallel to the base. What is the ratio of the volume of the            original cone to the volume of the smaller cone?  

      (a) 4:1

      (b) 8:1

      (c) 2:1 

      (d) 6:1

Answer:- (b) 8:1

50. If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then        the ratio of their heights will be

     (a) 3 : 8

     (b) 8 : 3

     (c) 9 : 2

     (d) 8 : 1

     (e) None of the above

Answer:-  (b) 8 : 3

51. The ratio of the radius and height of a 2 ^ cone is 5 : 12. Its volume is 314— cm . Its 7 slant            height is ?

     (a) 18 cm 

     (b) 13 cm

     (c) 16 cm

     (d) 15 cm

     (e) None of the above

Answer:-  (b) 13 cm

52. If the height of the right circular cone is increased by 200% and the radius of the base is                  reduced by 50%, then the volume of the cone ?

      (a) increases by 25%

     (b) increases by 50%

     (c) remains unchanged

     (d) decreases by 25%

     (e) None of the above

Answer:- (d) decreases by 25%

53. If the volumes of two right circular cones are in the ratio 1 : 3 and their diameters are in the          ratio  3 : 5, then the ratio of their heights is  ?

     (a) 25 : 27

     (b) 1 : 5

     (c) 3 : 5 

     (d) 5 : 27

Answer:-  (a) 25 : 27

54. The diameters of two cones are equal. If their slant heights be in the ratio of 5 : 7, then find            the  ratio of their curved surface areas.  

      (a) 25 : 7

      (b) 25 : 49

      (c) 5 : 49

      (d) 5 : 7

Answer:-  (d) 5 : 7

55. A conical cap has the base diameter 24 cm and height 16 cm. What is the cost of painting the         surface of the cap at the rate of 70 paise per sq cm?  

    (a) 520 

    (b)  524 

    (c) 528 

    (d) 532

Answer:-  (c) 528 

56. The curved surface area and the total surface area of a cylinder are in the ratio 1 : 2. If the              total  surface area of the right cylinder is 616 cm , then its volume is

     (a) 1632 cm3

     (b) 1078 cm3

     (c) 1232 cm3

     (d) 1848 cm3

Answer:-  (b) 1078 cm3

 

Sphere

57. Weight of a solid metallic sphere of radius 4 cm is 4 kg. The weight of a hollow sphere made             with same metal, whose outer diameter is 16 cm and inner diameter is 12 cm, is ?

       (a) 20.5 kg

       (b) 15.5 kg

       (c) 16.5 kg

       (d) 18.5 kg

Answer:-  (d) 18.5 kg

58. If the radius of a sphere is increased by 100%, by what per cent does its volume increase?

      (a) 300% 

      (b) 900%

      (c) 500%

      (d) 700%

      (e) None of the above

Answer:- (d) 700%

59. If radius of a sphere is decreased by 24%, by what per cent does its surface area decrease? 

      (a) 44%

      (b) 49% 

      (c) 42.24%

      (d) 46.2% 

       (e) None of the above

Answer:- (c) 42.24%

60. What will be the surface area of the sphere having 4 cm radius?

       (a) 64 sq cm

      (b) 69 sq cm

      (c) 32  sq cm

      (d) 35 sq cm

Answer:- (a) 64 sq cm

61. What is the diameter of the largest circle lying on the surface of a sphere of surface area 

       616 sq cm?

      (a) 14 cm

      (b) 10.5 cm

      (c) 7 cm

       (d) 3.5 cm

Answer:- (a) 14 cm

62. The diameter of the Moon is approximately one-fourth of the diameter of the Earth. What is          the ratio (approximate) of their volumes?

      (a) 4:16 

      (b)1:64 

      (c)2:6

      (d)1:128

 Answer:-     (b)1:64 

63. If the radius of a sphere is increased by 3%, then what per cent increase takes place in surface        area  of the sphere? 

      (a) 6.09%

      (b) 7%

      (c) 5.06% 

      (d) 9%

      (e) None of the above

Answer:- (a) 6.09%

64. A metallic sphere of radius 12 cm is melted into three smaller spheres. If the radii of two                  smaller spheres are 6 cm and 8 cm, the radius of the third is

      (a) 14 cm 

      (b) 16 cm

      (c) 10 cm 

      (d) 12 cm

Answer:- (c) 10 cm 

65. Find the number of lead balls of diameter 2 cm each, that can be made from a sphere of                  diameter  16cm.

      (a) 2048 

      (b) 512

      (c) 2002

      (d) 1520

       (e) None of the above

Answer:-  (b) 512

66. A hemispherical bowl has 3.5 cm radius. It is to be painted inside as well as outside. Find the          cost of painting it at the rate of  5 per 10 sq cm.

      (a) 50

      (b) 81

      (C)  56

      (d)  77 

      (e) None of the above

Answer:- (d)  77 

67. If the surface area of a sphere is 616 sq cm, what is its volume?

      (a) 4312/3 cm3

      (b) 4102/3 cm3

      (c) 1257 cm3

      (d) 1023 cm3

Answer:- (a) 4312/3 cm3

68. If the ratio of the diameters of two spheres is 3 : 5, then what is the ratio of their surface                  areas?  

      (a) 9 : 25 

      (b) 9 : 10

      (c) 3 : 5 

      (d) 27 : 125

Answer:- (a) 9 : 25 

69. If 64 identical small spheres are made out of a big sphere of diameter 8 cm, what is surface              area of each small sphere?

      (a) 兀 cm2

      (b) 2兀 cm2

      (c) 4兀cm2

      (d) 8兀  cm2

Answer:- (c) 4兀cm2

70. A hemisphere has 28 cm diameter. Find its curved surface area. 

      (a) 1232 sq cm 

     (b) 1236 sq cm

     (c) 1238 sq cm

     (d) 1233 sq cm

Answer:- (a) 1232 sq cm 

 71. What will be the difference between total surface area and curved surface area of a                           hemisphere having 2 cm diameter?

      (a) 2兀  sq cm

      (b) 3兀 sq cm

      (c) 兀 sq cm 

      (d) 4兀  sq cm

      (e) None of the above

Answer:-  (c) 兀 sq cm 

 

  

 

 

Volume and Surface Area Mathematic

 

Volume and Surface Area Mathematic

Volume and Surface Area Mathematic

Important information:- Volume and surface area are related to solids or hollow bodies. These bodies occupy space and have usually three dimensions length, breadth and height.

 #Volume:-  Space occupied by an object is called the 'volume' of that particular object. It is always measured in cube unit like cubic meter, cubic centimeter  etc.

#Surface Area:- Surface area of a solid body is the area of all of its surfaces together. Surface area is measured in square unit like square centimeter , square meter etc.

#Cube:- A solid body having 6 equal faces with equal length, breadth and height is called a cube. Infact, each face of a cube is a square.

#Cuboid:- A rectangular solid body having 6 rectangular faces is called a cuboid

#Room:- A rectangular room has 4 walls (surfaces) and opposite walls have equal areas.

#Box:-  A box has its shape like cube or cuboid. The amount that a box can hold or contain, is called the capacity of the box. Infact , capacity is the internal volume

#Cylinder:- A cylinder is a solid or hollow body that is formed by keeping circles of equal radii one on another. Apart from this, a cylinder is formed by rolling a rectangular sheet also. A cylinder has three surfaces  .

Table of Contain:-   

# If the volume of a cube is 729 cu cm, what is the length of its diagonal? 

#A metal box measures 20 cm x 12 cm x 5 cm. Thickness of the metal is 1 cm. Find the volume         of the metal required to make the box.

# The whole surface area of a rectangular block is 8788 sq cm. If length, breadth and height are        in the ratio of 4 : 3 : 2, then find the length.

#How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge? 

#If each side of a cube is decreased by 19%, then decrease in surface area is  ?

#If the side of a cube is increased by 12%, by how much per cent does its volume increase?

1. The side of a cube measures 9 cm. What will be the diagonal of the cube (in cm)?

    (a) 5√ 3

    (b) 7√ 3 

    (c) 9√ 3

    (d) 3√ 3

    (e) None of the above 

Answer:- (c) 9√ 3

2. The diagonal of a cube is 2√ 3 cm. Find the surface area of the cube.

    (a) 15 sq cm

    (b) 18 sq cm

    (c) 25 sq cm 

    (d) 24 sq cm

    (e) None of the above

Answer:- (d) 24 sq cm

 3. If the total surface area of a cube is 6 sq units, then what is the volume of the cube? [CDS 2013]

    (a) 1 cu unit

    (b) 2 cu units

    (c) 4 cu units 

    (d) 6 cu units 

Answer:-  (a) 1 cu unit

4. If the volume of a cube is 729 cu cm, what is the length of its diagonal? [CDS 2012] 

    (a) 9√ 2 cm

    (b) 9√ 3 cm 

    (c) 18 cm 

    (d) 18√ 3 cm

Answer:-  (b) 9√ 3 cm 

 5. Find the surface area of a cuboid 10 m long, 5 m broad and 3 m high. [Bank Clerks 2008]

     (a) 105 sq m 

     (b) 104 sq m 

     (c) 170 sq m 

     (d) 190 sq m 

      (e) None of the above 

Answer:- (d) 190 sq m 

6. The surface area of a cube is 726 sq cm. Find the volume of the cube. [SSC (10+2) 2008]

    (a) 1331 cm3

    (b) 1232 cm3

    (c) 1626 cm3

    (d) 1836 cm3 

Answer:- (a) 1331 cm3

7. The volume of a cuboid is 1989 cm , while its length and breadth are 17 cm and 13 cm,                     respectively. Find the height of the cuboid.

     (a) 9 cm

     (b) 4 cm

     (c) 14 cm

     (d) 7 cm 

     (e) None of the above 

Answer:-  (a) 9 cm

8. Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find half of the                surface area of the new cube.

    (a) 243 sq cm 

    (b) 463 sq cm 

    (c) 486 sq cm 

    (d) 293 sq cm

    (e) None of the above 

Answer:-  (a) 243 sq cm 

9. The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm x 6         cm x 2 cm, is ?

     (a) 2√ l3 cm 

     (b) 2√ 14 cm 

     (c) 2√ 26 cm 

     (e)2√ 2cm

Answer:- (c) 2√ 26 cm 

 10. Internal length, breadth and height of a rectangular box are 10 cm, 8 cm and 6 cm,                           respectively. How many boxes are needed which can be packed in a cube whose volume is               6240 cu. cm.? 

       (a) 12 

       (b) 13 

       (c) 15 

       (d) 17 

Answer:- (b) 13 

11. A metal box measures 20 cm x 12 cm x 5 cm. Thickness of the metal is 1 cm. Find the volume         of the metal required to make the box.

     (a) 550 cm3

     (b) 656 cm3 

     (c) 660 cm3 

     (d) 475 cm3

     (e) None of the above

Answer:- (c) 660 cm3 

 12. How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge? 

       (a) 63 

       (b) 432

       (c) 216 

       (d) None of these

Answer:- (c) 216 

 13. A cube has each edge 2 cm and a cuboid is 1 cm long, 2 cm wide and 3 cm high. The paint in a         certain container is sufficient to paint an area equal to 54 cm . Which one of the following is           correct? 

      (a) Both cube and cuboid can be painted

      (b) Only cube can be painted

      (c) Only cuboid can be painted 

      (d) Neither cube nor cuboid can be painted 

Answer:- (a) Both cube and cuboid can be painted

14. The whole surface area of a rectangular block is 8788 sq cm. If length, breadth and height are        in the ratio of 4 : 3 : 2, then find the length.

     (a) 26 cm

     (b) 52 cm 

     (c) 104 cm 

     (d) 13 cm 

Answer:- (b) 52 cm 

15. If the areas of three adjacent faces of a cuboidical box are 120 sq cm, 72 sq cm and 60 sq cm,          respectively, then find the volume of the box.

      (a) 820 cm3 

      (b) 720 cm3 

       (c) 750 cm3

       (d) 750 cm3

       (e) None of the above 

Answer:- (b) 720 cm3 

16. The capacity of a cuboid tank of water is 50000 L. Find the breadth of the tank, if its length            and depth are 2.5 m and 10 m, respectively. 

      (a) 2 m 

      (b) 4 m

      (c) 9 m

      (d) 6 m

      (e) None of the above

Answer:- (a) 2 m 

 17. The paint in certain container is sufficient to paint an area equal to 9.375 sq m. How many              bricks of dimensions 22.5 cm x 10 cm x 7.5 cm can be painted out of this container?

        (a) 100 

        (b) 200 

        (c) 50 

        (d) 175 

        (e) None of the above

Answer:- (a) 100 

 18. What are the dimensions (length, breadth and height, respectively) of a cuboid with volume           720 cu cm, surface area 484 sq cm and the area of the base 72sqcm?  

       (a) 9, 8 and 10 cm

       (b) 12, 6 and 10 cm 

       (c) 18, 4 and 10 cm

       (d) 30, 2 and 12 cm 

Answer:-  (a) 9, 8 and 10 cm

19. The volume of a cube is numerically equal to sum of its edges. What is the total surface area            in  square units? 

      (a) 12 

      (b) 36 

      (c) 72 

      (d) 144 

Answer:- (c) 72 

20. If each side of a cube is decreased by 19%, then decrease in surface area is  ?

      (a) 40% 

      (b) 38.4%

      (c) 35% 

      (d) 34.39% 

      (e) None of the above 

Answer:- (d) 34.39% 

21. If the side of a cube is increased by 12%, by how much per cent does its volume increase?

     (a) 40.4928%

     (b) 50.5240%

     (C) 60.3292%

     (d) 30.4928%

     (e) None of the above 

Answer:- (a) 40.4928%

Cylinder 

22. Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm. 

      (a) 1400 cm3

      (b) 1553 cm3

      (c) 12320 cm3 

      (d) 13320 cm3

      (e) None of the above 

Answer:- (c) 12320 cm3 

23. The diameter of the base of a right circular cylinder is 14 cm, while its length is 40 cm. Find            the total surface area of the cylinder. ?

      (a) 2068 sq cm 

      (b) 1825 sq cm 

      (c) 1925 sq cm

       (d) 2160 sq cm

       (e) None of the above

Answer:-  (a) 2068 sq cm 

24. If the lateral surface area of a cylinder is 94.2 sq cm and its height is 5 cm, then find the                  radius  of its base. (7t = 3.14) 

      (a) 5 cm

      (b) 8 cm

      (c) 3 cm 

      (d) 4 cm 

       (e) None of the above

Answer:-  (c) 3 cm 

 25. A rod of 2 cm diameter and 30 cm length is converted into a wire of 3 m length of uniform              thickness. The diameter of the wire is ? 

      (a) 2√ 10 cm

      (b) 2 /√ l0 cm

      (c)1/√ 10cm 

      (d) 1√ 10 cm 

Answer:-  (b) 2 /√ l0 cm

26. What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm? 

      (a) 10 cm

      (b) 12 cm

      (c) 15 cm

      (d) 16 cm

Answer:-  (d) 16 cm

 27. What will be the curved surface area of a right circular cylinder having length 160 cm and              radius of the base is 7 cm?  

        (a) 6020 sq cm 

        (b) 5052 sq cm 

        (c) 7045 sq cm 

        (d) 7040 sq cm 

        (e) None of the above 

Answer:- (d) 7040 sq cm 

 28. The ratio of the radii of two cylinders is 2 : 3 and the ratio of their heights is 5 : 3. The ratio           of  their volumes will be  ?

       (a) 4 : 9 

       (b) 9 : 4 

       (c) 20 : 27 

       (d) 27 : 20 

Answer:- (c) 20 : 27 

29. The curved surface area of a cylindrical pillar is 264 sq m and its volume is 924 m . The ratio          of its diameter to its height is ?

      (a) 7 : 3

      (b) 3 : 7 

      (c) 7 : 6 

      (d) 6 : 7 

      (e) None of the above 

Answer:- (a) 7 : 3

30. If height of cylinder is decreased by 8%, while its radius remains unchanged, by what per              cent  does the volume decrease? 

     (a) 4%

     (b) 6% 

     (c) 8% 

     (d) 10% 

     (e) None of the above 

Answer:- (c) 8% 

31. If the radius of a cylinder is increased by 25% and its height remains unchanged, then find            the  per cent increase in volume. 

      (a) 56.25% 

      (b) 52.25%

      (c) 50.4% 

      (d) 60.26%

      (e) None of the above 

Answer:- (a) 56.25% 

32. If the radius of a cylinder is decreased by 8%, while its height is increased by 4%, what will            be  the effect on volume?

      (a) 11.9744% (decrease)

      (b) 11.9744% (increase) 

      (c) 12.4678% (decrease)

      (d) 12.4678% (increase)

      (e) None of the above 

Answer:-  (a) 11.9744% (decrease)

 33. A drainage tile is a cylindrical shell 21 cm long. The inside and outside diameters are 4.5 cm           and 5.1 cm, respectively. What is the volume of the clay required for the tile? 

       (a) 15.7 兀 cm3 

       (b) 25.2 兀 cm3

       (c) 30.24 兀   cm3

      (d) None of these 

Answer:- (c) 30.24 兀   cm3

34. The diameter of a roller is 84 cm and its length 120 cm. It takes 500 complete revolutions to             move once over to level a playground. Find the area of the playground (in sq m).

       (a) 1632

       (b) 1817 

       (c) 1532 

       (d) 1584

       (e) None of the above 

Answer:-  (d) 1584

35. A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the                curved surface of the piller at the rate of  10 per sq m. [Bank Clerks 2010] 

      (a)  50

      (b)  68

      (c)  98 

      (d)  55

      (e) None of the above 

Answer:- (d)  55

36. A piller 14 cm in diameter is 5 m high. How much material was used to construct it? [Bank            Clerks 2010]

      (a) (77 x 10^2 ) cm3 

     (b) (77 x 10^4 ) cm3

     (c) (77 x 10^5 )cm3 

     (d) (77 x 10^3 )cm3

     (e) None of the above 

 Answer:- (d) (77 x 10^3 )cm3

Car Air-conditioning System

       *Car Air-conditioning System

CAR AIR-CONDITIONING SYSTEMS Some of the important air-conditioning systems used and manufactured by Ford and general Motors are given here:

Ford Air-conditioning System:-

This system uses a factory installed unit. It has the blower, heat exchangers and housing on the engine side of the finned wall. A thermostat expansion valve with a built in sight glass and a two cylinder compressor usually mounted horizontally is used. There are two service valves mounted on the head of the compressor. A thermostat having its sensitive bulb clamped to the evaporator fins operates the compressor magnetic clutch. For providing the air circulation, duct dampers operated by a vacuum activating system are used.

General Motors Air-conditioning System:-

This system uses a rotary compressor. To control the evaporator pressure and exhaust muffler on the compressor, a pressure operated altitude valve is used. Basic refrigeration circuit of automatic air-conditioning system consists of an electrically controlled heating system, air cooling system and air duct flow using a vacuum activator system for controlling the dampers and the valves. Three temperature sensors (one outside the car, one inside the car and another in the discharge disc) connected to an amplifier and a programmer are used in this system.

Major components and refrigerant flow of the air conditioning system for Maruti MF 410 vehicle is shown

in picture

The recent research has called for a ban on 'R134a' refrigerantalso and to replace the same with CO2. In addition to the environmental benefits, CO, as a refrigerant has also the following advantages: 

1. 20% less fuel consumption than today's systems, due to better average efficiency throughout the year.

2. Cooling capacity of the present air conditioning systems is limited by the compressor piston displacement, which itself is limited by the insufficient space in the engine compartment. CO, air conditioning systems only need about 13% of the volume flow of an 'R134a' system, making it possible to use smaller compressors enabling CO, system to cool the passenger compartment faster.

3. As the process is also reversible, unlike today's air conditioners, it also has a heat pump function. This can be used to heat up the vehicle interior very quickly. replacing the electric supplemental heaters that are common with modern direct-injection diesel engines.

It is expected that due to the above clear advantages, CO₂ technology will start replacing present air conditioners in 2007. 'Luk' has specialized in the development of compressors for the new technology.

Important tips for the maintenance of car AC system are:

1. Clean the condenser during normal servicing. Clogged condenser can result in frequent AC tripping and lesser cooling.

2. Maintain correct refrigerant level. Less refrigerant would result in less cooling. Excessive refrigerant would also result in lesser cooling and excessive tripping.

3. Top up the compressor with adequate oil.

4. Clean the evaporator periodically. Clogging of evaporator would cause poor airflow and hence lesser cooling.

5. Maintain proper belt tension. A loose belt will slip whereas overtight belt would cause noise and premature compressor failure.

Important precautions while using car AC systems are:

1. Do not use AC with fresh air mode open always since this mode is for occasional use just to release the air in circulation for a long time. Frequent use of fresh air mode may result in the accumulation of dust and clogging of evaporators.

2. Never operate AC with heater on.

3. Never run AC without refrigerant, otherwise compressor may cease. 4. Do not leak-test AC with more than 2 MPa pressure,

higher pressure can damage the components.

5. Do not leave AC joints open, which may cause the moisture to enter the system. 6. Do not charge the refrigerant in the AC system before flushing.

 7. Do not switch on the AC at high speeds, which may result in the ceasing of compressor.

Bus Air-conditioning:-

Air-conditioning system used for a bus is of standard design. Its condensing unit is very compact and is generally installed in the bus in such a way that for servicing it is readily accessible. Due to large size of the unit, a separate gasoline engine with an automatic starting device is used to drive the compressor. To permit sliding of the condensing unit out of the bus body during servicing the condensing unit is generally mounted on rails with flexible suction and liquid lines. Standard thermostat expansion valves refrigerant controls and air cooled condensers are used. Evaporator used are finned blower. The ducts, usually one on each side of the bus. run between a false ceiling and roof of the bus. Grills controlled by passengers are provided at their seats.

TRUCK AIR-CONDITIONING:-

Due to varying conditions of heating, ventilating, cooling and dehumidification in the atmosphere at various places, long distance hauling trucks and truck tractors carrying perishable products are air-conditioned. Air-conditioned equipment used is of the "hang on" type. It is generally installed after the body has been made. Generally, two evaporators, one on the cab and other for product compartment, are used. A remote condenser mounted on the roof of the cab is generally used. To enable the radiator to operate at fuel efficiency, it helps to remove the condenser from infront of the radiator.

ROVAC AIR-CONDITIONER:-

This system of air-conditioning of the car uses air. It is yet to be commercially deployed in cars. The system has been designed by Dr. Thomas C. Edwards. It is rotary vane air cycle air-conditioning system. The system has the following distinguishing features:

1. It does not use Freon gas. Hence, there is no high pressure gas to store, seal against leaks or replace. The system is thus much simpler.

2. It has high coefficients of performance when compared with conventional type. This makes the system to consume less power of engine and hence there is fuel economy.

3. It gives instant cold. There is no detectable time lag from start up to cold air.

4. It gives instant heat. This makes the heat available from intermediate coils for defrosting long before the engine gets warmed up.

ROVAC system alternately compresses and expands the air. The conventional sealed units make use of reversed Rankine cycle with a gas-to- liquid and back-to-gas phase change. ROVAC uses no phase change like the conventional sealed units, except for the incidental moisture normally present in the air. Edwards calls this a reversed Brayton cycle.

The oval shaped housing acts as a compressor on the inlet side and an expander on the exhaust side. The air enters the compressor at atmospheric pressure and passenger compartment temperature. This air is compressed to a pressure of about 21N/cm and temperature of about 140° C. From the compressor, the air travels through heat exchanger which is provided with fins. In fact, the heat exchanger has large tubes. The inside air is cooled by the outside air flowing past the tubes. This drops the temperature of inside air to 45° C. There is no appreciable change in the pressure.

Now, this air is lead through the expander where the pressure drops to atmospheric and the temperature of the air drops to about 6° C. This air is circulated inside the passenger compartment, thus cooling the occupants. The cycle gets repeated.

It may be mentioned that the ROVAC can be designed to produce outlet temperatures well below freezing point. Modulation and moisture control is handled in the distribution ducts. It is worth mentioning that when the hot air is passing through the expander, it returns part of its heat energy to the vaned rotor, thus saving engine power.

  *Car Air-conditioning System