1. 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.

2. 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.

3. If the curved surface area of a right circular cylinder is 264 square meters and its volume is 924 cubic meters, then what is the radius of the base?

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

5. If the curved surface area of a right circular cylinder is \( a \) square units, the radius of its base is \( r \) units, and the volume is \( v \) cubic units, then determine the value of \( \cfrac{ar}{v} \).

6. If the curved surface area of a right circular cylinder is \(C\) square units, the radius of the base is \(r\) units, and the volume is \(V\) cubic units, then determine the value of \(\cfrac{Cr}{V}\).

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

8. 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 = _____.

9. If the curved surface area of a right circular cylinder is 440 cm² and its volume is 1540 cm³, what is its radius?

(a) 5 cm (b) 6 cm (c) 7 cm (d) 8 cm

10. 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, determine the value of \( \cfrac{Cr}{V} \).

11. If the curved surface area of a right circular cylinder is \(S\), its volume is \(V\), and its radius is \(r\), then the value of \(\cfrac{Sr}{V}\) is -

(a) 2 (b) 4 (c) 8 (d) none of the above

12. If the radius of a right circular cylinder is 2 units, then for any height of the cylinder, the numerical values of its volume and curved surface area are equal.

13. If the radius of a right circular cylinder is 2 units, then for any height of the cylinder, the numerical values of its volume and curved surface area are equal.

14. If the height of a right circular cylinder is 14 cm and its curved surface area is 264 square cm, then find its volume.

15. If the numerical value of the curved surface area and the volume of a sphere are equal, then the radius will be 3 units.

16. If the radius of a right circular cylinder is doubled and the height is halved, then the curved surface area of the new cylinder will be what fraction of the original cylinder’s curved surface area?

(a) equal (b) double (c) half (d) four times

17. If the numerical values of the volume and the curved surface area of a right circular cylinder are equal, then the diameter of the cylinder is ___________ units.

18. A right circular cone has its **volume equal to its curved surface area**. If the height and radius of the cone are respectively **h units** and **r units**, then **show that**: \[ \frac{1}{h^2} + \frac{1}{r^2} = \frac{1}{9} \]

19. Translate: "If a right circular cylinder has lateral surface area \(c\) square units, base radius \(r\) units, and volume \(V\) cubic units, then find the height (value) of the cylinder." Would you like me to solve it too? I’m ready when you are.

20. 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) \(18\pi \, cm^2\)

21. 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 \(\frac{1}{h^2} + \frac{1}{r^2}\).

22. If the total surface area and the volume of a cube are numerically equal, then the length of its edge will be -- units.

23. The curved surface area of a right circular cone is \(\sqrt{5}\) times its base area. The ratio of its height to radius will be _____.

24. 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) \(1:\sqrt2\)

25. 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

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

27. The curved surface area of a right circular cylinder is 440 square cm, and its volume is 1540 cubic cm. Find the height of the cylinder.

28. If the height and diameter of a right circular cylinder are equal, and its volume is 2156 cubic cm, then find the radius.

(a) 5 cm (b) 6 cm (c) 7 cm (d) 9 cm

29. A rectangle has a length of \( a \) units and a breadth of \( b \) units. When the rectangle is wrapped to form a right circular cylinder, the circumference of the base of the cylinder is equal to the length of the rectangle. The lateral surface area of the cylinder will be _____.

30. If the height of a right circular cylinder is 14 cm and the curved surface area is 264 square cm, then what is the volume of the cylinder?