1. If a right circular cone has a height of 12 cm and a volume of \(100\pi\) cubic cm, then what is the radius of the cone?

2. If the base radius of a right circular cone is 3 cm and the height is 4 cm, then the lateral surface area of the cone will be.

(a) \(10\pi \, cm^2\) (b) \(15\pi \, cm^2\) (c) \(12\pi \, cm^2\) (d) \(18\pi \, cm^2\)

3. If the volume of a right circular cone is \(100\pi\) cubic centimeters and its height is 12 cm, then what is its slant height?

(a) 13 cm (b) 16 cm (c) 9 cm (d) 26 cm

4. If a right circular cone has a height of \(12\) cm and a volume of \(1024\pi\) cubic cm, what is the slant height of the cone?

(a) 20 cm (b) 21 cm (c) 22 cm (d) 23 cm

5. A solid cylindrical iron rod has a cross-sectional diameter of 16 cm and a length of 1 meter. If this rod is melted and used to form right circular cones, each with a height of 4 cm and a base radius of 5 cm, how many such cones can be made?

6. If the volume of a cone with a height of 12 cm is 154 cubic cm, then what will be the radius of its base?

(a) 3.5 cm (b) 4.5 cm (c) 5 cm (d) 5.5 cm

7. If the radius of a right circular cone is halved and its height is doubled, then the volume of the cone will be — of its original volume.

8. If the volume of a right circular cone is \(100\pi\) cubic cm and its height is 12 cm, find the slant height of the cone.

9. 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

10. "A hollow right circular cylinder has an external diameter of 16 cm and an internal diameter of 12 cm. Its height is 36 cm. If it is melted and recast into solid cylinders, each with a diameter of 2 cm and a height of 6 cm, calculate and write how many such solid cylinders can be made."

11. The radius of a solid right circular iron rod is 32 cm and its length is 35 cm. If the rod is melted and recast into solid cones each with a radius of 4 cm and height of 28 cm, calculate how many such cones can be made.

12. If the volume of a right circular cone is \(100π\) cubic cm and its height is 12 cm, calculate and write the slant height of the cone.

13. "The height of a right circular cone is 12 cm and its volume is \(100π\) cubic cm. Write the length of the radius of the cone."

14. The volume of a right circular cone is V. If both the height and the radius are doubled, the new volume will be:

(a) 3V (b) 4V (c) 6V (d) 8V

15. A right circular cone has a base radius of 20 cm and a height of 10 cm. If it is melted down, how many solid spheres of radius 2 cm can be made from it?

(a) 200 (b) 100 (c) 250 (d) 125

16. If the radius of a right circular cone is kept constant and its height is increased by 10%, by what percentage will the volume increase?

(a) 10% (b) 11% (c) 12% (d) 14%

17. A solid vertical cylindrical cone has both its diameter and height equal to 21 cm. Find the volume of the largest possible sphere that can be obtained from this cone. Also, determine the ratio of the volumes of the cone and the sphere.

18. 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?

19. A right circular cone has a height of 12 cm and a volume of \(100\pi\) cubic cm. Find the slant height of the cone.

20. If a right circular cone has a vertical angle of 60° and a radius of 7 cm, what is its curved surface area?

(a) 400 square centimetre (b) 350 square centimetre (c) 325 square centimetre (d) 308 square centimetre

21. If the radius of a right circular cylinder is 2 units, then for any height, the numerical values of the cylinder’s volume and curved surface area will be equal.

22. If the slant height of a right circular cone is 15 cm and the diameter of its base is 16 cm, then the lateral surface area of the cone is –

(a) \(60\pi\) square cm (b) \(68\pi\) square cm (c) \(120\pi\) square cm (d) \(130\pi\) square cm

23. If a solid iron sphere has a radius of 12 cm, how many cone-shaped objects of 2 cm radius and 3 cm height can be formed by melting the sphere?

24. A right circular drum has a radius of 21 cm and a height of 2i. A solid iron sphere has a diameter of 21 cm. Determine the ratio of the volumes of the drum and the solid iron sphere (neglecting the thickness of the drum). Now, if the drum is completely filled with water and the sphere is fully submerged and then removed, determine the new depth of the water in the drum.

25. If both the radius and height of a right circular cylinder are doubled, its volume will be four times the original volume.

26. If a right circular cone has a base radius of 6 cm and a half-vertex angle of 30°, then its height is _____ cm.

27. The volume of a right circular cone is 180\(\pi\) cubic cm, and its height is 15 cm. Find the length of the base diameter.

28. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:2, then their radius ratio will be –?

29. If the height of a right circular cone remains the same and its radius is doubled, the volume of the cone will increase by 300%.

30. The slant height of a right circular cone is 7 cm, and the total surface area is 147.84 cm². Determine the radius of its base.