Volume and Surface Area Mathematic
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| 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:-
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 å…€ cm3
(b) 25.2 å…€ cm3
(c) 30.24 å…€ cm3
(d) None of these
Answer:- (c) 30.24 å…€ 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
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