1. 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

2. 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

3. 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.

4. If a right circular cone has a vertex angle of 60° and a base radius of 14 cm, then what is the curved surface area of the cone?

(a) 1680 square cm (b) 1232 square cm (c) 1080 square cm (d) 1442 square cm

5. If a right circular cone and a sphere have the same radius, and the numerical value of the cone's volume is equal to the numerical value of the sphere's curved surface area, then what is the height of the cone?

(a) 10 units (b) 11 units (c) 12 units (d) 13 units

6. If a right circular cone has a base diameter of 7 cm and a slant height of 10 cm, what is the total surface area of the cone?

(a) 184.5 square cm (b) 185.4 square cm (c) 148.5 square cm (d) 184.6 square cm

7. 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?

8. 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.

9. 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

10. 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

11. 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.

12. "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."

13. If a right circular cone has a vertex angle of 60° and a base radius of 14 cm, what is the curved surface area of the cone?

14. A vertical hollow cylindrical pipe made of iron has both ends open. Its height is 35 cm, the outer radius is 12 cm, and the inner radius is 10 cm. What is the volume of iron in the pipe in cubic centimeters?

15. 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) \(18\pi \, cm^2\)

16. The radius of the base of a right circular cone is equal to the radius of a sphere. The volume of the cone (in cubic centimeters) is equal to the curved surface area of the sphere (in square centimeters). What is the height of the cone?

(a) 4 cm (b) 3 cm (c) 8 cm (d) 12 cm

17. Two solid spheres with radii of 8 cm and 10 cm are melted to form a right circular cone with a height of 42 cm. What is the radius of the cone?

(a) 8 cm (b) 10 cm (c) 12 cm (d) 16 cm

18. A sphere and a right circular cone have the same radius \(r\) and equal volume. What is the height of the cone?

(a) \(\cfrac{r}{3}\) (b) \(\cfrac{r}{4}\) (c) \(\cfrac{3r}{4}\) (d) \(\cfrac{4r}{3}\)

19. 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.

20. If the volume of a right circular cone is \(X\) cubic units, the area of its base is \(Y\) square units, and its height is \(Z\) units, then what is the value of \(\frac{YZ}{X}\)?

21. If the radius of a right circular cone is decreased by 50% and its height is increased by 50%, what is the percentage change in the volume of the cone?

22. If the height of a right circular cone is 14 cm and its curved surface area is 264 cm², what is the volume of the cone?

23. A solid right circular cone and a solid sphere have the same radius and the same volume. What is the ratio of the diameter of the sphere to the height of the cone?

(a) \(2 : 1 \) (b) \(1 : 2\) (c) \(1 : 1\) (d) \(2 : 3\)

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

26. If a right circular cone has a volume of \(x\) cubic units and a base area of \(y\) square units, then its height is _____.

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 volume of a right circular cone is \(V\) cubic units, the area of the base is \(A\) square units, and the height is \(H\), then what is the value of \(\frac{AH}{V}\)?

29. If the height of a right circular cylinder is 14 cm and the curved surface area is 264 square cm, then what is the volume of the cylinder?

30. The height of a solid right circular cone is 20 cm and its slant height is 25 cm. If a solid right circular cylinder of height 15 cm has the same volume as the cone, then calculate and write the diameter of the base of the cylinder.