1. 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

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

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

4. 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

5. 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?

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

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 height of a right circular cone remains the same and its radius is doubled, the volume of the cone will increase by 300%.

10. 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

11. 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

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 a right circular cone is halved and its height is doubled, then the volume of the cone will be — of its original volume.

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

15. 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.

16. 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!

17. 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) \(18\pi \, cm^2\)

18. 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

19. 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

20. 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

21. If the radii of two cones are in the ratio 2:3 and their heights are in the ratio 5:3, then what will be the ratio of their volumes?

(a) 4:9 (b) 9:4 (c) 27:20 (d) 20:27

22. The numerical value of the volume and the lateral surface area of a right circular cone are equal. If the height and radius of the cone are \( h \) units and \( r \) units respectively, find the value of \[ \left( \frac{1}{h^2} + \frac{1}{r^2} \right) \]

23. 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.

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

25. A cone and a cylinder with the same base radius and the same height will have the cone's volume equal to half the volume of the cylinder.

26. If the volumes of two cones are in the ratio \(1:4\) and their radii are in the ratio \(4:5\), then what will be the ratio of their heights?

(a) 1:5 (b) 5:4 (c) 5:16 (d) None of the above

27. 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.

28. 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?

29. If \(h\), \(s\), and \(v\) represent the height, curved surface area, and volume of a right circular cone respectively, then the value of \(3πVh^3 – s^2h^2 + 9V^2\).

(a) 16\(\pi\) (b) 0 (c) 4\(\pi\) (d) 32\(\pi^2\)

30. The volume and the lateral surface area of a right circular cone are numerically equal. If the height and radius of the cone are \(h\) and \(r\) units respectively, write the value of \(\frac{1}{h^2} + \frac{1}{r^2}\).