1. 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?

- 6.96π cubic cm
- 6.76π cubic cm
- 5.76π cubic cm
- None of the above

2. 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

- 370 cm
^{3}and 380 cm^{3} - 380 cm
^{3}and 390 cm^{3} - 390 cm
^{3}and 400 cm^{3} - None of the above

3. If x is the curved surface area and y is the volume of a right circular cylinder, then which one of the following is correct?

- The ratio of height to radius of the cylinder is independent of x only
- The ratio of height to radius of the cylinder is independent of y only
- Either (a) or (b)
- Neither (a) nor (b)

4. A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m, while the vertex of the cone is 16 m above the ground. What is the area of the curved surface for conical portion?

- 3434/9 square metre
- 3431/8 square metre
- 3432/7 square metre
- 3234/7 square metre

5. What is the height of a solid cylinder of radius 5 cm and total surface area is 660 cm ^{2}?

- 10 cm
- 12 cm
- 15 cm
- 16 cm

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

- 264π cubic cm
- 252π cubic cm
- 236π cubic cm
- None of the above

7. 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?

- 1 : 16
- 1 : 12
- 1 : 8
- 1 : 4

8. A cylindrical tank 7 m in diameter, contains water to a depth of 4 m. What is the total area of wetted surface?

- 110 m
^{2} - 126.5 m
^{2} - 131.5 m
^{2} - 136.5 m
^{2}

9. A cylindrical vessel of height 10 cm has base radius 60 cm. If d is the diameter of a spherical vessel of equal volume, then what is d equal to?

- 30 cm
- 60 cm
- 90 cm
- 120 cm

10. From a solid cylinder of height 4 cm and radius 3 cm, a conical cavity of height 4 cm and of base radius 3 cm is Followed out. What is the total surface area of the remaining solid?

- 15π square cm
- 22π square cm
- 33π square cm
- 48π square cm

11. The radii of two cylinders are in the ratio 2 : 3 and their curved surface areas are in the ratio 5 : 3. What is the ratio of their volumes?

- 20 : 27
- 10 : 9
- 9 : 10
- 27 : 20

12. 10 cylindrical pillars of building have to be painted. The diameter of each pillar is 70 cm and the height is 4 m. What is the cost of painting at the rate of Rs. 5 per square metre?

- Rs. 400
- Rs. 440
- Rs. 480
- Rs. 500

13. The curved surface of cylinder is 1000 cm^{2}. A wire of diameter 5 mm is wound around it, so as to cover it completely. What is the length of the wire used?

- 22 m
- 20 m
- 18 m
- None of the above

14. A cylindrical rod of iron whose radius is one-fourth of its height is melted and cast into spherical balls of the same radius as that of the cylinder. What is the number of spherical balls?

- 2
- 3
- 4
- 5

15. A solid cylinder of height 9 m has its curved surface area equal to one-third of the total surface area. What is the radius of the base?

- 9 m
- 18 m
- 27 m
- 30 m

16. Half of a large cylindrical tank open at the top is filled with water and identical heavy spherical balls are to be dropped into the tank without spilling water out. If the radius and the height of the tank are equal and each is four times the radius of a ball, what is the maximum number of balls that can be dropped?

- 12
- 24
- 36
- 48

17. A cylinder having base of circumference 60 cm is rolling without sliding at a rate of 5 rounds per second. How much distance will the cylinder roll in 5 seconds?

- 15 m
- 1.5 m
- 30 m
- 3 m

18. The inner and outer radii of a 7 m long hollow iron right circular cylindrical pipe are 2 cm and 4 cm respectively. If 1000 cm^{3} of iron weighs 5 kg, what is the weight of the pipe?

- 264 kg
- 132 kg
- 396 kg
- None of the above

19. A container is in the form of a right circular cylinder surmounted by a hemisphere of the same radius 15 cm as the cylinder. If the volume of the container is 32400π cm ^{3}, then the height h of the container satisfies which one of the following?

- 135 cm < h < 150 cm
- 140 cm < h < 147 cm
- 145 cm < h < 148 cm
- 139 cm < h < 145 cm

20. A cylindrical can of internal diameter 24 cm contains water. A solid sphere of radius 6 cm is completely immersed in water in the cylinder. The water level increases by

- 0.25 cm
- 0.5 cm
- 2 cm
- 3 cm

21. From a cylindrical log whose height is equal to its diameter, the greatest possible sphere has been taken out. What is the fraction of the original log which is cut away?

- 1/2
- 1/3
- 1/4
- 2/3

22. A cylindrical vessel of base radius 14 cm is filled with water to some height. If a rectangular solid of dimensions 22 cm x 7 cm x 5 cm is immersed in it, what is the rise in water level?

- 0.5 cm
- 1.0 cm
- 1.25 cm
- 1.5 cm

23. A lead pencil is in the shape of a cylinder. The pencil is 21 cm long with radius 0.4 cm and its lead is of radius 0.1 cm. What is the volume of wood in the pencil?

- 9 cm
^{3} - 9.4 cm
^{3} - 9.9 cm
^{3} - 10.1 cm
^{3}

24. A hollow cylindrical iron pipe of length 1.4 m has bore radius 2.5 cm and thickness of the metal is 1 cm. What is the volume of the iron used in the pipe?

- 2640 cm
^{3} - 2604 cm
^{3} - 2460 cm
^{3} - None of the above