1. The number of surfaces of a solid right circular cylinder is _____.
2. The number of surfaces of a right circular cylinder is _____.
3. The number of surfaces of a solid right circular cylinder is 3.
4. 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 _____.
5. The number of surfaces of a solid elliptical cylinder is _____.
6. A solid sphere is melted and recast into a solid right circular cylinder. The volumes of the sphere and the cylinder are_______.
7. A right circular cylinder and a right circular cone have equal base radii and equal heights. The ratio of their volumes is _________.
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 volumes of two right circular cylinders of equal height are in the ratio 16:25, then what is the ratio of their radii?
(a) 4:5 (b) 5:4 (c) 3:5 (d) 5:3
10. 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
11. What is the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere, all having the same diameter and the same height?
12. The curved surface area of a right circular cylinder is 440 square centimeters. If the height of the cylinder is 10 centimeters, find its volume.
13. A right circular cylinder made of iron sheet is open at both ends. Its height is 42 cm, thickness is 1 cm, and its outer radius is 10 cm. Find the amount of iron used to make the cylinder.
14. If a right circular cylinder has a radius of 3 cm and a height of 4 cm, then what is the length of the longest rod that can be placed inside it?
15. A hollow metallic sphere has an inner radius of 3 cm and an outer radius of 5 cm. It is melted to form a solid right circular cylinder of height \(\frac{8}{3}\) cm. Find the diameter of the base of the cylinder.
16. 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?
17. If the ratio of the heights of two right circular cylinders is 1:2 and the ratio of their base circumferences is 3:4, then the ratio of their volumes will be 9:32.
18. If a solid sphere is melted to form a solid right circular cylinder, then the _____ of the sphere and the cylinder will be equal.
19. A right circular cylinder has a height-to-base-radius ratio of 3:1. If the volume of the cylinder is \(1029\pi\) cubic cm, find the total surface area of the cylinder.
20. A right circular cylinder and a cone have equal bases, and the ratio of their volumes is 3:2. Prove that the height of the cone is half the height of the cylinder.
21. A right circular cylinder and a right circular cone have equal base radii and equal heights. The ratio of their volumes = ___________.
22. A hollow right circular cylinder has an outer diameter of 16 cm and an inner diameter of 12 cm. The height of the cylinder is 36 cm. If it is melted down, how many solid cylinders of diameter 2 cm and height 5 cm can be made from it?
23. 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 ______.
24. 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?
25. 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
26. 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 \(\frac{cr}{v}\).
27. 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.
28. The curved surface area of a right circular cylinder is 264 square meters, and its volume is 924 cubic meters. Find the diameter and height of the cylinder.
29. Two right circular cylinders have a height ratio of 1:2 and a base circumference ratio of 3:4. What is the ratio of their volumes?
30. A solid right circular cone is melted to form a solid right circular cylinder of the same radius, with a height of \(5\) cm. Determine the height of the cone.
(a) 10 cm (b) 15 cm (c) 18cm (d) 24cm
