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volumes MCQs

Practise focused volumes questions with marked answers for exam preparation and subject revision.

volumes Mcqs
1. If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
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A. 600

B. 500

C. 900

D. 1000
2. The area of the cardboard(in cm<sup>2
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A. 1390 cm2

B. 695 cm<sup>2</sup>

C. 1280 cm<sup>2</sup>

D. 1220 cm<sup>2</sup>

3. A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is_________?
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A. 2:05

B. 1: 3

C. 3:01

D. 3:05

4. The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area?
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A. 1:02

B. 2:01

C. 1:4

D. 4:01

5. If the volume and surface area of a sphere is numerically the same then its radius is_________?
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A. 3 units

B. 4 units

C. 1 unit

D. 2 units

6. If the volumes of two cubes are in the ratio 8: 1, the ratio of their edges is_________?
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A. 2 : 1

B. None of these

C. 8:01

D. 2?2 : 1

7. The surface area of a cube is 726m<sup>2
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A. 1542 m<sup>3</sup>

B. 1452 m<sup>3</sup>

C. 1331 m3

D. 1300 m<sup>3</sup>

8. Surface area of two spheres are in the ratio 1:4 what is the ratio of their volumes?
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A. 0.086111111

B. 1:04

C. 1:8

D. 8:01

9. The radius of a circular cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder is________?
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A. Equal to its radius

B. Equal to its diameter

C. 4/3 times its radius

D. 2/3 times its radius

10. The sides of a cube are in the ratio 1:2 the ratio of their volume is__________?
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A. 2:01

B. 1:04

C. 1:02

D. 1:8
11. The number of solid spheres each of diameter 6 cm, that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm is?
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A. 3

B. 5

C. 6

D. 4

12. A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?
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A. 12 cm

B. 18 cm

C. 10 cm

D. 24 cm

13. If the length, breadth and the height of a cuboid are in the ratio 6: 5: 4 and if the total surface area is 33300 cm<sup>2
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A. 90, 85, 60

B. 85, 75, 60

C. 90, 75,60

D. 90, 75, 70

14. If the height of a cone is increased by 100% then its volume is increased by_________?
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A. 200%

B. 400%

C. 300%

D. 100%
15. A cylinder and a cone have a same height and same radius of the base. The ratio between the volumes of the cylinder and cone is__________?
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A. 2:01

B. 1:02

C. 1:03

D. 3:1
16. A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 20 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the level of the field will raise by nearly?
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A. 0.29 cm

B. 0.299 cm

C. 4.15 cm

D. 2.98 cm
17. A wooden box of dimensions 8m x 7m x 6m is to carry rectangular boxes of dimensions 8cm x 7cm x 6cm. The maximum number of boxes that can be carried in 1 wooden box is?
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A. 7500000

B. 1200000

C. 1000000

D. 9800000

18. Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
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A. 6000

B. 4000

C. 5000

D. 7000

19. A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?
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A. 3000 M<sup>3</sup>

B. 4500 M3

C. 2700 M<sup>3</sup>

D. 27000 M<sup>3</sup>

20. The length of the wire of 0.2mm radius that can be drawn after melting a solid copper sphere of diameter 18cm?
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A. 2430 m

B. 243 m

C. 24300 m

D. 24.3 m

21. A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
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A. 22000

B. 23000

C. 24000

D. 25000
22. The radius of a wire is decreased to one third if volume remains the same length will increase
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A. 3 times

B. 1 Time

C. 6 times

D. 9 times
23. The length of the longest rod that can fit in a cubical room of 4 m side is?
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A. 5.196 m

B. 8.66 m

C. 6.928 m

D. 7.264 m

24. The diameters of two spheres are in the ratio 1:2 what is the ratio of their volumes?
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A. 9:16

B. 1:8

C. 4:03

D. 3:04

25. In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be_________?
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A. 10000 cu.m

B. 2000 cu.m

C. 100 cu.m

D. 1000 cu.m
26. The height of two right circular cones are in the ratio 1:2 and their perimeters of their bases are in the ratio 3:4, the ratio of their volume is_________?
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A. 3:08

B. 0.419444444

C. 9:32

D. 9:16

27. A metal sheet 27 cm long 8cm broad and 1 cm thick is melted into a cube. The difference between the surface areas of two solids is__________?
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A. 300 cm<sup>2</sup>

B. 296 cm<sup>2</sup>

C. 286 cm2

D. 284 cm<sup>2</sup>

28. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
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A. 344.35 cm2

B. None of these

C. 344.35 cm2

D. 344.35 cm2

29. Find the ratio between whole surfaces of a sphere and a hemisphere?
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A. 3:01

B. 4:3

C. 3:04

D. 1:03

30. The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.
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A. 48 ? cm2

B. 24 ? cm<sup>2</sup>

C. 36 ? cm<sup>2</sup>

D. 74 ? cm<sup>2</sup>

31. The area of a base of a cone is 30 cm<sup>2
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A. 50 cm<sup>3</sup>

B. 40 cm<sup>3</sup>

C. 120 cm<sup>3</sup>

D. 60 cm3
32. The ratio of the volumes of a cube to that of the sphere which will fit inside the cube is________?
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A. 4:04

B. 6: ?

C. 4:03

D. 4:02

33. Find the length of the wire required to go 15 times round a square field containing 69696 m<sup>2
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A. 15820 m

B. 15640 m

C. 15840 m

D. 16840 m

34. A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone then the height of the cylinder is________?
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A. 4h

B. 2h/3

C. 3h/2

D. 2h

35. A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
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A. 3:02

B. 2:01

C. 25 : 18

D. 27:20:00

36. The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?
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A. 1:8

B. 1:16

C. 1:04

D. 0.086111111

37. Find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2.
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A. 1:2

B. 4:01

C. 1:04

D. 2:01

38. The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid.
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A. 5 cm

B. 13 cm

C. 144 cm

D. 19 cm

39. The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
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A. 440 sq cm

B. 132 sq cm

C. 220 sq cm

D. 308 sq cm

40. If the sides of two cubes are in the ratio 3: 1 the ratio of their total surface area is?
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A. 12:01

B. 8:01

C. 3:01

D. 9:1
41. If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm<sup>2
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A. 7?

B. 60?

C. 100?

D. 50?

42. A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m<sup>2
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A. Rs.57

B. Rs.60

C. Rs.52

D. Rs.55

43. What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
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A. 15 cm

B. 13 cm

C. 12 cm

D. 10 cm

44. The surface of a cube is 24sq cm. Find its volume?
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A. 32 cc

B. 64 cc

C. 8 cc

D. 16 cc

45. The edge of a cube is 2a cm. Find its surface?
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A. 24a2cm2

B. 12a<sup>2</sup>cm<sup>2</sup>

C. 6a<sup>2</sup>cm<sup>2</sup>

D. 8a<sup>2</sup>cm<sup>2</sup>

46. Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
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A. 19 cm

B. 21 cm

C. 32 cm

D. 18 cm
47. The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface?
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A. 18 ?r<sup>2</sup>sq units

B. 3 ?r<sup>2</sup>sq units

C. 12 ?r2sq units

D. 6 ?r<sup>2</sup>sq units

48. The area of the floor of a room is 20 m<sup>2
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A. 60 m3

B. 100 m<sup>2</sup>

C. 400 m<sup>3</sup>

D. 450 m<sup>3</sup>

49. The curved surface of a sphere is 64 ? cm<sup>2
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A. 2 cm

B. 1 cm

C. 4 cm

D. 3 cm

50. The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
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A. 7:06

B. 7 : 3

C. 3:07

D. 6:07