1. If the radius of the base of a right circular cone is halved and its height is doubled, the volume of the cone remains the same.

2. If the radius of the base of a right circular cone is halved and its height is doubled, the volume of the cone will remain the same.

3. If the radius of the base of a tall circular cone is halved and the height is doubled, the volume of the cone remains the same.

4. 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.

5. 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%.

6. If the height of a right circular cone remains unchanged and its radius is increased by 1 unit, the volume of the cone becomes four times its original volume. What is the length of the diameter of the cone?

7. 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

8. If the base area of a right circular cone is \(A\), its height is \(H\), and its volume is \(V\), then express \(H\) in terms of \(V\) and \(A\).

(a) \(H=\cfrac{3V}{A}\) (b) \(H=\cfrac{V}{A}\) (c) \(H=\cfrac{V}{3A}\) (d) \(H=\cfrac{3V}{2A}\)

9. 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%

10. The radius of the base of a solid right circular cone is equal to the radius of a solid sphere. If the volume of the sphere is twice the volume of the cone, find the ratio of the height of the cone to the radius of its base.

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

12. 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 \(\frac{YZ}{X}\)?

13. If the volume of a right circular cone is \(V\), the area of its base is \(A\), and its height is \(H\), then find the value of \(\left(\frac{AH}{V}\right)^2\).

(a) 1 (b) 4 (c) 9 (d) 3

14. 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?

15. The radius of a right circular cone is reduced by 50% and its height is increased by 50%. By what percentage does the volume of the cone change?

16. Find the radius of the base of a right circular cone if its slant height is 7 cm and its total surface area is 147.84 cm².

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

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

19. 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.

20. 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.

21. The slant height of a right circular cone is 7 cm, and its total surface area is 147.84 square cm. Find the radius of its base.

22. Here's the English translation: **"If the radius of a right circular cone is kept unchanged but its height is doubled, by what percentage will its volume increase?"** Let me know if you'd also like help solving it!

23. The slant height of a right circular cone is 7 cm and its total surface area is 147.84 square cm. Find the radius of the base and the area of the base of the cone. Let me know if you'd like the full solution worked out as well. I'm happy to help.

24. 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 \(\frac{AH}{V}\)?

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

26. The slant height of a right circular cone is 7 cm and its total surface area is 147.84 sq. cm. Find the radius of the base of the cone.

27. 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.

28. A solid sphere with a radius of \(r\) units is melted and recast into a solid right circular cone with a height of \(r\) units. Find the radius of the base of the cone.

(a) 2r units (b) 3r units (c) r unit (d) 4r units

29. The base radius of a solid right circular cone is \(r\) units, its vertical height is \(h\) units, and its slant height is \(l\) units. The cone’s base is attached to the base of a solid right circular cylinder. If the base radius and height of the cylinder are equal to those of the cone, then the total surface area of the combined solid is \((πrl + 2πrh + 2πr^2)\) square units.

30. The radius of the base of a solid right circular cone is equal to the radius of a solid sphere. If the volume of the sphere is twice the volume of the cone, then write the ratio of the height of the cone to the radius of its base.