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

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

3. If the curved surface area of a right circular cylinder is \(c\) square units, the base radius is \(r\) units, and the volume is \(v\) cubic units, then the value of \(\frac{cr}{v}\) is = _____.

4. 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) \(18\pi \, cm^2\)

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. The ratio of the base radii of two right circular cones is 2 : 3, and the ratio of their heights is 3 : 2. Then the ratio of their volumes is —

(a) 3:2 (b) 9:4 (c) 4:9 (d) 2:3

7. 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) \(H=\cfrac{3V}{2A}\)

8. 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?

9. 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 \(\frac{AH}{V}\).

10. 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.

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

12. 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

13. If the ratio of the heights of two right circular cones is 1:4 and the ratio of their radii is 2:1, then the ratio of their volumes will be ______.

14. If a right circular cone has volume \(V\) cubic units and base area \(A\) square units, then the height is _____.

15. 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.

16. The lateral surface area of a right circular cone with a base radius of 1.5 meters and a slant height of 14 meters is _____.

(a) 66 square meters (b) 22 square meters (c) 44 square meters (d) 88 square meters

17. The lateral surface area of a right circular cone with a base radius of 1.5 meters and a slant height of 14 meters is _____.

(a) 66 square meters (b) 22 square meters (c) 44 square meters (d) 88 square meters

18. 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.

19. 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.

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

21. 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 \(\frac{AH}{V}\).

22. 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.

23. If a solid cone and a solid right circular cylinder have the same base radius and same height, and the ratio of their curved surface areas is 5:8, then determine the ratio of their base radius to height.

24. 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.

25. 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.

26. A right circular cylinder and a right circular cone have equal base radii and equal heights. The ratio of their volumes is _________.

27. Here's the English translation of your sentence: **If the volume of a right circular cone is V cubic units and the base area is A square units, then the height is -----** If you'd like, I can help you fill in the blank or derive the formula for the height! ????

28. 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

29. If the radius of a right circular cone is \(\cfrac{r}{2}\) units and the slant height is \(2l\) units, then the total surface area is –

(a) \(2πr (l+r)\) square units (b) \(πr\left(l+\cfrac{r}{4}\right)\) square units (c) \(πr(l+r)\) square units (d) \(2πr l\) square units

30. 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