Volume and Surface Area Mathematic 2
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| 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:-
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 å…€ cm3 (b) 6 å…€ cm3 (c) 4.5å…€ cm3 (d) 3.7 å…€ cm3 Answer:- (c) 4.5å…€ 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 å…€cm3 (b) 2527 å…€cm3 (c) 1224 å…€cm3 (d) None of these Answer:- (c) 1224 å…€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 å…€ cm3 (b) 2500å…€ cm3 (c) 5000/3å…€ cm3 (d) 5000 å…€cm3 Answer:- (a) 2500/3 å…€ 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
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