level – 1

1. The circumference of the base of a circular cylinder is 20π cm. The height of the cylinder is equal to the radius of the base. How many litres of water can the cylinder hold?
(a) 5
(b) 8
(c) 10
(d) 12

2. The diameter of the base of a cylindrical tank is 28 dm and its height is 20 dm. The tank is full of oil. How many rectangular tins, each of size 20 cm × 25 cm × 28 cm, can be completely filled with the oil from the tank? (Take π = 22/7)
(a) 800
(b) 900
(c) 1000
(d) 1100

3. Spherical balls of diameter 2 cm are dropped into a cylindrical vessel containing some water and are completely submerged. The diameter of the vessel is 14 cm. If the water level rises by 6 cm, how many balls are dropped into the vessel? (Take π = 22/7)
(a) 210
(b) 252
(c) 294
(d) 336

4. A right circular cone is completely filled with water. How many right circular cylinders, each having the same base radius and height as the cone, are required to store the water?
(a) 1
(b) 2
(c) 3
(d) 4

5. Water flows at the rate of 7 metres per minute from a cylindrical pipe of diameter 10 mm. How long will it take to fill a conical vessel whose base diameter is 28 cm and height is 21 cm?
(a) 18 minutes
(b) 21 minutes
(c) 24 minutes
(d) 28 minutes

6. If the radius of a cylinder is increased by 20% and its height is decreased by 25%, then the change in the volume of the cylinder is:
(a) 10% increase
(b) 20% increase
(c) 20% decrease
(d) no change

7. The amount of concrete required to build a solid cylindrical pillar whose base has a perimeter of 14 m and whose curved surface area is 42 m², is: (Take π = 22/7)
(a) 14 m³
(b) 21 m³
(c) 28 m³
(d) 35 m³

level – 2

1. A cylindrical tank of diameter 28 cm is full of water. If 8.8 litres of water is drawn off, the level of water in the tank will drop by : (Take π = 22/7)
(a) 10 cm
(b) 12 cm
(c) 14 cm
(d) 16 cm

2. Rainwater from a rectangular roof measuring 14 m × 10 m drains completely into a cylindrical tank of diameter 2 m and height 2.8 m. If the tank is just full, the rainfall (in cm) is: (Take π = 22/7)
(a) 2 cm
(b) 3 cm
(c) 4 cm
(d) 5 cm

level – 3

1. Two right circular cylinders have equal volumes. If the ratio of their heights is 4 : 1, then the ratio of their radii is:
(a) 1 : 2
(b) 2 : 1
(c) 1 : 4
(d) 4 : 1

2. The volume of a right circular cylinder whose height is 28 cm and whose circumference of the base is 44 cm, is: (Take π = 22/7)
(a) 6160 cm³
(b) 7392 cm³
(c) 8624 cm³
(d) 9856 cm³

3. The base radii of two right circular cylinders are in the ratio 3 : 5 and their heights are in the ratio 10 : 9. The ratio of their volumes is:
(a) 1 : 1
(b) 2 : 3
(c) 3 : 5
(d) 5 : 9

4. The curved surface area of a cylindrical pillar is 176 m² and its volume is 616 m³. (Take π = 22/7) The ratio of the diameter of the pillar to its height is:
(a) 2 : 1
(b) 3 : 2
(c) 4 : 3
(d) 5 : 3

5. A hollow cylindrical pipe is 14 cm long. The external diameter of the pipe is 10 cm and the internal diameter is 6 cm. The volume of metal used (in cm³) is: (Take π = 22/7)
(a) 704
(b) 792
(c) 880
(d) 968

6. A hollow iron pipe is 14 cm long and its external diameter is 6 cm. If the thickness of the pipe is 1 cm and the density of iron is 8 g/cm³, then the weight of the pipe is: (Take π = 22/7)
(a) 1408 g
(b) 1568 g
(c) 1792 g
(d) 2016 g

7. The volume of a right circular cylinder, 7 cm in height, is equal to that of a cube whose edge is 7 cm. (Take π = 22/7), the radius of the base of the cylinder is:
(a) 3 cm
(b) 3.5 cm
(c) 4 cm
(d) 5 cm

8. The length of the pipe is 14 cm and its external radius is 8 cm. (Take π = 22/7), then the thickness of the pipe is:
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

9. The volume of the metal of a cylindrical pipe is 880 cm³. The length of the pipe is 14 cm and its external radius is 8 cm. (Take π = 22/7), then the thickness of the pipe is:
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

10. The volume of the metal of a cylindrical pipe is 616 cm³. The length of the pipe is 14 cm and its external radius is 7 cm. (Take π = 22/7) then the thickness of the pipe is:
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

11. The radii of the bases of two cylinders P and Q are in the ratio 4 : 3 and their heights are in the ratio n : 1. If the volume of cylinder P is 4 times the volume of cylinder Q, then the value of n is:
(a) 2
(b) 3
(c) 4
(d) 6

12. Water flows through a circular pipe whose internal diameter is 14 cm. If the speed of flow of water is 5 cm per second, how many litres of water are pumped out in 1 hour? (Take π = 22/7)
(a) 1100 L
(b) 1540 L
(c) 1760 L
(d) 2200 L

13. The lateral surface area of a cylinder is 880 cm² and its height is 10 cm. Find the volume of the cylinder. (Take π = 22/7)
(a) 1540 cm³
(b) 1750 cm³
(c) 2200 cm³
(d) 3080 cm³

14. The diameters of two right circular cylinders whose volumes are equal are in the ratio 4 : 3. The ratio of their heights is:
(a) 9 : 16
(b) 16 : 9
(c) 4 : 3
(d) 3 : 4

15. From a solid cylinder of height 14 cm and radius of the base 7 cm, a cone of the same height and same base is removed. The volume (in cm³) of the remaining solid is:
(a) 1437
(b) 2156
(c) 2874
(d) 3593

16. From a solid cylinder of height 21 cm and diameter 14 cm, a conical cavity of the same height and same base diameter is hollowed out. The volume (in cm³) of the remaining solid is: (Take π = 22/7)
(a) 2940
(b) 3080
(c) 3430
(d) 3528

17. The radius of a cylinder is 7 cm and its height is 14 cm. The number of centimetres that should be added either to the radius or to the height so that the increase in volume is the same in both cases is:
(a) 2
(b) 3
(c) 4
(d) 7

18. The radii of the bases of a cylinder and a cone are in the ratio √5 : √3 and their heights are in the ratio √3 : √5. The ratio of their volumes is:
(a) 5 : 3
(b) 3 : 5
(c) 10 : 3
(d) 5 : 6

19. The curved surface area and the total surface area of a right circular cylinder are in the ratio 2 : 3. If the total surface area of the cylinder is 942 cm², then the volume of the cylinder is:
(a) 1078 cm³
(b) 1232 cm³
(c) 1540 cm³
(d) 1760 cm³

20. A right circular cylinder has the same radius and volume as a sphere of diameter 14 cm. The height of the cylinder is:
(a) 7 cm
(b) 14/3 cm
(c) 28/3 cm
(d) 49/3 cm

21. A conical vessel of internal radius 9 cm and height 42 cm is completely filled with water. The water is poured into a cylindrical vessel of internal radius 7 cm. The height to which the water rises in the cylindrical vessel is:
(a) 18 cm
(b) 21 cm
(c) 24 cm
(d) 27 cm

22. The volume of a right circular cylinder is equal to the volume of a right circular cone whose height is 48 cm and diameter of the base is 14 cm. If the height of the cylinder is 12 cm, then the diameter of its base is:
(a) 14 cm
(b) 16 cm
(c) 18 cm
(d) 20 cm

23. A rectangular sheet of paper measuring 28 cm × 14 cm is rolled to form a cylinder along its length. The volume of the cylinder formed is:
(a) 616 cm³
(b) 784 cm³
(c) 882 cm³
(d) 1232 cm³

24. A rectangular sheet of paper measuring 88 cm × 28 cm is rolled to form a cylinder along its length. The volume of the cylinder formed is:
(a) 4312 cm³
(b) 4928 cm³
(c) 5390 cm³
(d) 6160 cm³

25. A cone, a hemisphere, and a cylinder stand on equal circular bases and have the same height. If the radius of the base is 7 cm, then the ratio of their volumes is:
(a) 1 : 2 : 3
(b) 2 : 3 : 4
(c) 3 : 4 : 5
(d) 1 : 3 : 5

26. Water flows at a speed of 4 km/h through a pipe of diameter 7 cm into a rectangular tank of dimensions 40 m × 35 m. How much time (in hours) will it take for the water level in the tank to rise by 5 cm?
(a) 2 hours
(b) 3 hours
(c) 4 hours
(d) 5 hours

27. The total surface area of a solid right circular cylinder is three times the surface area of a solid sphere. If both solids have the same radius, then the ratio of the volume of the cylinder to that of the sphere is:
(a) 3 : 1
(b) 9 : 4
(c) 12 : 5
(d) 27 : 8

28. A solid sphere of radius 5 cm is completely immersed in a cylindrical vessel of diameter 20 cm containing water. The increase in the height of the water level (in cm) is:
(a) 1.5
(b) 2
(c) 2.5
(d) 3

29. From a right circular cylinder of radius 7 cm and height 24 cm, a right circular cone of the same base radius is removed. If the volume of the remaining solid is 3080 cm³, then the height of the removed cone is:
(a) 12 cm
(b) 14 cm
(c) 18 cm
(d) 21 cm

30. Let A denote the volume of a right circular cylinder whose height is equal to twice its radius, and B denote the volume of a sphere of the same radius. Then the value of A/B is:
(a) 1
(b) 3/2
(c) 2
(d) 4/3

31. If the radius of a cylinder is decreased by 20% and its height is increased by 25%, then the volume of the new cylinder compared to the original volume will be decreased by:
(a) 25%
(b) 30%
(c) 40%
(d) 50%

32. A well of radius 7 m is dug to a depth of 10 m. The earth taken out is spread uniformly all around the well to form an embankment of width 3 m. The height of the embankment is:
(a) 4 m
(b) 5 m
(c) 6 m
(d) 7 m

33. Two solid cylinders of radii 3 cm and 5 cm, and heights 14 cm and 6 cm respectively, are melted and recast into a cylindrical disc of thickness 2 cm. The radius of the disc is:
(a) 7 cm
(b) 8 cm
(c) 9 cm
(d) 10 cm

34. A solid metallic cone is melted and recast into a solid cylinder having the same base radius as that of the cone. If the height of the cone is 21 cm, then the height of the cylinder is:
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm

35. A cylindrical pencil of diameter 2 cm has one of its ends sharpened to form a conical shape of height 3 cm. The volume of the material removed is:
(a) 3.14 cm³
(b) 4.19 cm³
(c) 6.28 cm³
(d) 12.56 cm³

36. A solid right circular cylinder has a total surface area of 264 cm². If its curved surface area is 3/4 of its total surface area, then the volume of the cylinder is: (Take π = 22/7)
(a) 294 cm³
(b) 308 cm³
(c) 336 cm³
(d) 352 cm³

37. The radius of a wire is reduced to one-half of its original radius. If the volume of the wire remains the same, the length of the wire will increase by:
(a) 100%
(b) 200%
(c) 300%
(d) 400%

38. The number of coins of radius 1 cm and thickness 0.5 cm required to be melted to make a right circular cylinder of height 10 cm and base radius 2 cm is:
(a) 60
(b) 80
(c) 100
(d) 120

39. A cylindrical container of height 21 cm and radius 10 cm is completely filled with sand. The sand is poured out to form a conical heap of height 14 cm. The radius of the base of the conical heap is:
(a) 12 cm
(b) 15 cm
(c) 18 cm
(d) 21 cm

40. A cylindrical vessel of radius 5 cm contains water. A solid sphere of radius 4 cm is gently dipped into the vessel until it is completely immersed. By how much will the water level rise in the vessel?
(a) 3.2 cm
(b) 4 cm
(c) 5.12 cm
(d) 6.4 cm

41. The sum of the radius and height of a solid right circular cylinder is 18 cm. If its total surface area is 792 cm², then the volume of the cylinder is:
(a) 756 cm³
(b) 864 cm³
(c) 924 cm³
(d) 1008 cm³

42. A right circular cylinder is partially filled with water. Two solid spherical balls are completely immersed in the water, causing the water level to rise by 8 cm. If the radius of one ball is twice that of the other and the radius of the cylinder is 6 cm, then the radii of the two spherical balls are:
(a) 1 cm and 2 cm
(b) 2 cm and 4 cm
(c) 3 cm and 6 cm
(d) 4 cm and 8 cm

43. The radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5 : 2. The ratio of their volumes is:
(a) 40 : 27
(b) 80 : 27
(c) 20 : 9
(d) 16 : 9

44. If the volumes of two right circular cones are in the ratio 2 : 9 and the radii of their bases are in the ratio 2 : 3, then the ratio of their heights is:
(a) 1 : 3
(b) 2 : 3
(c) 3 : 2
(d) 1 : 2

45. The volume of a metallic hollow cylindrical pipe of uniform thickness is 660 cm³. Its length is 10 cm and its external radius is 7 cm. The thickness of the pipe is:
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

46. The radius of a wire is reduced to one-fourth of its original radius. If the volume of the wire remains the same, the length of the wire will increase by:
(a) 12 times
(b) 15 times
(c) 16 times
(d) 8 times

47. The height of a right circular cylinder is twice the radius of its base. If the height were four times the radius, the volume of the cylinder would increase by 1056 cm³. Find the radius of the base.
(a) 6 cm
(b) 7 cm
(c) 8 cm
(d) 9 cm

level – 4

1. If the height of a cylinder is increased by 20% and the radius of its base is decreased by 5%, then by what percent will its curved surface area change?
(a) increase by 14%
(b) increase by 15%
(c) increase by 16%
(d) increase by 18%

2. Water flows through a cylindrical pipe of radius 3.5 cm at a speed of 4 metres per second. Find the time (in seconds) taken to fill an empty water tank of height 2 m and area of base 10 m². (Take π = 22/7)
(a) 200
(b) 220
(c) 240
(d) 280

3. The height of a solid right circular cylinder is 8 metres. If twice the sum of the areas of its two end faces is equal to the curved surface area of the cylinder, then the radius of its base (in metres) is:
(a) 2
(b) 3
(c) 4
(d) 5

4. The height of a circular cylinder is increased 4 times and the base area is reduced to one-fourth of its original value. The factor by which the lateral (curved) surface area of the cylinder changes is:
(a) 1
(b) 2
(c) 3
(d) 4

5. The radius and height of a cylinder are in the ratio 3 : 4. If the volume of the cylinder is 528 cm³, then the curved surface area of the cylinder (in cm²) is:
(a) 396
(b) 440
(c) 528
(d) 660

6. The diameter of a 100 cm long roller is 70 cm. It makes 400 complete revolutions to level a ground. If the cost of levelling the ground is ₹2 per m², then the total cost of levelling the ground is:
(a) ₹35,200
(b) ₹44,000
(c) ₹49,000
(d) ₹56,000

7. The earth taken out is spread uniformly all around the well to form an embankment in the shape of a circular ring of width 3 m. The height of the embankment is:
(a) 0.5 m
(b) 1 m
(c) 1.5 m
(d) 2 m

8. The radius of a cylindrical water container is half of its height. If the inner curved surface area of the container is 440 cm², then the amount of water it can hold is: (Take π = 22/7)
(a) 770 cm³
(b) 924 cm³
(c) 1100 cm³
(d) 1540 cm³

9. A fair-ground tent is cylindrical up to a height of 4 m and conical above it. The diameter of the base is 28 m and the slant height of the conical part is 20 m. Find the total area of canvas required to make the tent. (Take π = 22/7)
(a) 1232 m²
(b) 1408 m²
(c) 1584 m²
(d) 1760 m²

ANSWERS