1. 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

2. If the radius and height of a cone are both doubled, the volume of the cone will increase to—

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

3. If both the height and radius of a cone are doubled, the volume of the cone will increase –

(a) tripled (b) five times (c) seven times (d) nine times

4. The volume of a cone is jointly proportional to the square of the radius of the base and its height. If the ratio of the radii of two cones is 2:3 and their heights are in the ratio 5:4, then find the ratio of their volumes.

5. If the radius and height of a cone are both doubled, its volume will increase by _____ times.

6. If both the radius and height of a cone are doubled, the volume of the cone will increase by _____ times the original volume.

7. If the numerical values of the volume and lateral surface area of a cone are equal, then the relationship between its height and base radius is?

(a) \(r^2-h^2=2^2\) (b) \(2r^2+h^2=3^2\) (c) \(r^2+h^2=3^2\) (d) none of the above

8. If the radius and the height of a cone are both doubled, the volume of the cone becomes ___ times the volume of the original cone.

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

9. If the radius and height of a cone are both doubled, the volume of the cone becomes — times the volume of the original cone. This sets up a comparison for calculating how much larger the cone’s volume becomes. Need help filling in the blank or want this phrased differently? I’m here for it! ????????

(a) 4 times (b) 6 times (c) 8 times (d) 12 times

10. If the radius and height of a right circular cone are both doubled, its volume increases.

(a) \(300\%\) (b) \(400\%\) (c) \(700\%\) (d) \(800\%\)

11. If the radius and height of a cone are each doubled, what will be the volume of the new cone in relation to the volume of the original cone?

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

12. 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) \(18\pi \, cm^2\)

13. If a hemisphere and a cone have equal base areas and equal heights, then what will be the ratio of their volumes?

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

14. 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

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

16. If the volumes of two cones are in the ratio 2:3 and the ratio of their base radii is 1:2, then what is the ratio of their heights?

(a) 3:8 (b) 8:3 (c) 3:4 (d) 4:3

17. If the base area of a cone is \(x\) square units, its height is \(y\) units, and its volume is \(z\) cubic units, then what is the value of \(\frac{xy}{z}\)?

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

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 \(X\) 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 two cones have equal base radii and their heights are in the ratio 2:3, then the ratio of their volumes will be ______.

22. 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

23. 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.

24. If the height and the base radius of a right circular cone are equal, then the measure of the cone's apex angle will be _____.

25. The radius of a hemisphere and the height of a cone are equal. If their volumes are numerically equal, then what is the ratio of the radius of the hemisphere to the radius of the cone?

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. If the height and the radius of the base of a right circular cone are equal, then the vertex angle of the cone will be 90°.

28. 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.

29. 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.

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