1. 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.

2. If both the radius and the height of a cone are doubled, then the volume of the new cone will be how many times the volume of the original cone?

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

4. 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%.

5. 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.

6. If the radius of a right circular cylinder is halved and the height is doubled, the volume of the new cylinder will be what fraction of the original cylinder’s volume?

(a) equal (b) double (c) half (d) Four times.

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

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

8. 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

9. 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

10. 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

11. 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

12. 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%

13. 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.

14. A sphere and a right circular cylinder both have a radius of 3 cm. If their volumes are equal, what is the height of the cylinder?

15. 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.

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

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

18. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:4, then their radius ratio will be—.

(a) \(2:1\) (b) \(\sqrt2:1\) (c) \(1:2\) (d) \(1:\sqrt2\)

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

20. The numerical value of the volume and the lateral surface area of a right circular cone are equal. If the height of the cone is \( h \) and the radius is \( r \), determine the value of \(\cfrac{1}{h^2}+\cfrac{1}{r^2}\).

21. 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!

22. 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.

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

24. 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

25. If the radius and slant height of a right circular cone are both doubled, how many times will its total surface area increase?

26. 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) \(18\pi \, cm^2\)

27. 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

28. What is the ratio of the volumes of a right circular cylinder and a cone having the same radius and height?

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

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

30. 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) \(\cfrac{4r}{3}\)