1. If the ratio of the radii of two perpendicular solid cones is 2:3 and the ratio of their heights is 5:3, what is the ratio of their volumes ? (a) 27:20 (b) 20:27 (c) 4:9 (d) 9:4

2. The volumes of two perpendicular circular rings are equal. The ratio of their heights is 4:9, then what will be the ratio of their radii? (a) 3:2 (b) 2:3 (c) 4:9 (d) 8:9

3. From a rectangular tin sheet measuring 110 cm in length and 15 cm in width, a vertical cylindrical pipe of height 15 cm is to be made. What will be the diameter of the pipe? (a) 7 cm (b) 35 cm (c) 15 cm (d) 11.5 cm

4. If the radii of two cones are in the ratio 2:3 and their heights are in the ratio 5:3, then what will be the ratio of their volumes? (a) 4:9 (b) 9:4 (c) 27:20 (d) 20:27

5. A solid cone with a diameter of 16 cm and a height of 2 cm is melted to form 12 identical spheres. What is the diameter of each sphere? (a) \(\sqrt3\) cm (b) 2 cm (c) 3 cm (d) 4 cm

6. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be – (a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9

7. If the volumes of two vertical circular cylinders are equal, and their heights are in the ratio 4:9, then the ratio of their radii will be – (a) 3:2 (b) 2:3 (c) 4:9 (d) 8:9

8. If the volumes of two vertical solid cylinders are equal, and their heights are in the ratio 1:2, then the ratio of the lengths of their radii will be – (a) 1: √2 (b) √2:1 (c) 1:2 (d) 2:1

9. The outer and inner radii of an iron pipe are 4 feet and 3 feet respectively, and its length is 20 feet. If the weight of 1 cubic foot of iron is 10 kilograms, what is the weight of the pipe? (a) 4400 kg (b) 4040 kg (c) 4004 kg (d) 4000 kg

10. The outer and inner radii of a hollow cylinder are 11 cm and 10 cm respectively, and its height is 14 cm. What is the volume of the metallic part of the cylinder? (a) 880 cubic cm (b) 968 cubic cm (c) 88 cubic cm (d) 924 cubic cm

11. If the volumes of two solid right circular cylinders are equal and their heights are in the ratio 1:2, what will be the ratio of the lengths of their radii? (a) 1:√2 (b) √2:1 (c) 1:2 (d) 2:1

12. If a ring-shaped iron plate has inner diameter \(d_1\) and outer diameter \(d_2\), then the area of the plate will be: (a) \(\pi(d_1^2-d_2^2)\) (b) \(\cfrac{\pi}{4}(d_2^2-d_1^2)\) (c) \(\cfrac{\pi}{4}(d_1^2-d_2^2)\) (d) \(\cfrac{1}{4}(d_2^2-d_1^2)\)

13. If the volumes of two right circular cylinders of equal height are in the ratio 16:25, then what is the ratio of their radii? (a) 4:5 (b) 5:4 (c) 3:5 (d) 5:3

14. একটি চোঙের উচ্চতা 14 সেমি, এবং বক্রতলের ক্ষেত্রফল 594 বর্গ সেমি হলে তার ভূমির ব্যাসার্ধ হয় - translate in english (a) 6.25 cm (b) 6.50 cm (c) 6.75 cm (d) None of the above

15. If the height and diameter of a right circular cylinder are equal, and its volume is 2156 cubic cm, then find the radius. (a) 5 cm (b) 6 cm (c) 7 cm (d) 9 cm

16. Two right circular cones of equal height have their base diameters in the ratio 2 : 3. The ratio of their volumes will be — (a) 3:4 (b) 4:5 (c) 5:4 (d) 4:9

17. A hollow iron pipe has an inner radius of 3 feet and an outer radius of 4 feet. Its length is 20 feet. If the weight of 1 cubic foot of iron is 10 kilograms, what is the weight of the pipe? (a) 4400 kg (b) 4000 kg (c) 4040 kg (d) None of the above

18. If the volume and curved surface area of a right circular cylinder are numerically equal, then the radius of its base will be 1 unit. True / False

19. The number of surfaces of a solid right circular cylinder is 3. True / False

20. The curved surface area of a cylindrical wooden log of uniform density is 440 square decimeters. If one cubic decimeter of wood weighs 3 kilograms and the log weighs 18.48 quintals, find the diameter of the log.

21. A tall gas jar with a diameter of 7 cm contains some water. If a solid cylindrical iron piece with a diameter of 5.6 cm and a height of 5 cm is completely submerged in the water, how much will the water level rise?

22. A right circular cylinder has a height-to-base-radius ratio of 3:1. If the volume of the cylinder is \(1029\pi\) cubic cm, find the total surface area of the cylinder.

23. The difference between the outer and inner curved surface areas of a hollow cylindrical pipe is 44 square centimeters, and the length of the pipe is 14 cm. The volume of the material of the pipe is 99 cubic centimeters. Find the outer and inner radii of the pipe.

24. A conical water tank with a lid has a base area of 616 square meters and a height of 21 meters. Calculate the total surface area of the tank.

25. The curved surface area of a solid right circular cone is 1320 square centimeters. If the diameter of the base of the cone is 14 cm, find its height.

26. If the ratio of the radii of two vertical solid cylinders is 2:3 and the ratio of their heights is 5:3, then the ratio of their curved surface areas is 20:27.

27. Two vertical cylindrical vessels have equal volumes, and the ratio of their heights is 1:2. What is the ratio of the lengths of their radii?

28. If the curved surface area of a right circular cylinder is 264 square meters and its volume is 924 cubic meters, then what is the radius of the base?

29. An open cylindrical vessel has a total surface area of 2002 square centimeters. If the radius of its base is 7 cm, how many liters of water can it hold? (1 liter = 1 cubic decimeter)

30. The number of surfaces of a solid right circular cylinder is _____.

31. If the numerical value of the volume and the curved surface area of a right circular cone are equal, find the length of the diameter of the cone — in units.

32. If the ratio of the heights of two right circular cylinders is 1:2, and the ratio of the perimeters (circumferences) of their bases is 3:4, then find the ratio of their volumes.

33. The diameter of the cross-section of a wire is reduced by 50%. To keep the volume unchanged, by what percentage must the length of the wire be increased?

34. A rectangular sheet of paper has a length of \(l\) units and a breadth of \(b\) units. The sheet is rolled to form a right circular cylinder, where the circumference equals the length of the paper. The curved surface area of the cylinder is ____ square units.

35. A hollow cylindrical iron pipe is 6 meters long. Its internal and external diameters are 3.5 cm and 4.2 cm respectively. Calculate the volume of iron in the pipe. If the weight of iron is 5 kg per cubic decimeter, then find the total weight of the pipe.

36. A tall gas jar with a diameter of 10 cm contains some water. A solid cylindrical iron piece with a diameter of 8 cm and a height of 5 cm is completely submerged in the water. Determine how much the water level rises.

37. The number of surfaces of a right circular cylinder is _____.

38. Water flows through a pipe with a cross-sectional area of 3 square centimeters at a speed of 7.7 kilometers per hour. In 3\(\frac{1}{2}\) hours, it fills a reservoir completely. What is the volume of the reservoir?

39. A rectangle has a length of \( a \) units and a breadth of \( b \) units. When the rectangle is wrapped to form a right circular cylinder, the circumference of the base of the cylinder is equal to the length of the rectangle. The lateral surface area of the cylinder will be _____.

40. The lateral surface area of a right circular cylinder is equal to its volume. Determine the base area of the cylinder.

41. A solid rod has a length of \( h \) meters and a diameter of \( r \) meters. It is melted to form 6 spheres, each with a radius of \( r \) meters. Determine the relationship between \( h \) and \( r \).

42. A hollow vertical cylindrical iron pipe has an outer radius of 5 cm and an inner radius of 4 cm. If the total surface area of the pipe is 1188 square cm, what is the length of the pipe?

43. The curved surface area of a right circular cylinder is 440 square centimeters. If the height of the cylinder is 10 centimeters, find its volume.

44. A right circular cylinder made of iron sheet is open at both ends. Its height is 42 cm, thickness is 1 cm, and its outer radius is 10 cm. Find the amount of iron used to make the cylinder.

45. If a cone has volume \(V\) cubic units, total surface area \(S\) square units, height \(h\) units, and base radius \(r\) units, then show that: \[ S = 2V\left(\frac{1}{h} + \frac{1}{r}\right) \]

46. A fuel gas cylinder has an internal diameter of 2.8 decimeters and a height of 7.5 decimeters. If the weight of the gas is 325 grams per cubic decimeter, then how many kilograms of gas are in the cylinder?

47. A vertical circular cylinder has a height that is twice its radius. If the height were six times the radius, then the volume of the cylinder would be 539 cubic decimeters more. What is the height of the cylinder?

48. The number of surfaces of a solid elliptical cylinder is _____.

49. If a right circular cylinder has a radius of 3 cm and a height of 4 cm, then what is the length of the longest rod that can be placed inside it?

50. If the numerical value of the volume of a right circular cone is equal to the numerical value of its curved surface area, what is the radius of the cone?