1. The number of surfaces of a solid right circular cylinder is _____.
2. The number of surfaces of a solid right circular cylinder is _____.
3. The number of surfaces of a right circular cylinder is _____.
4. The ratio of the radii of two right circular solid cylinders is 2:3, and the ratio of their heights is 5:3. Find the ratio of their curved surface areas.
5. 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?
6. 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.
7. If a solid sphere is melted to form a solid right circular cylinder, then the _____ of the sphere and the cylinder will be equal.
8. 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?
9. 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
10. The ratio of the base radii of a right circular cylinder and a right circular cone is 3:4, and the ratio of their heights is 2:3. What will be the ratio of the volumes of the cylinder and the cone?
11. 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) \(1:\sqrt2\)
12. A solid hemisphere and a solid right circular cylinder have the same height and the same base radius. Determine the ratio of their curved surface areas.
13. A solid right circular cone is melted to form a solid cylinder of the same radius, with a height of 5 cm. Find the height of the cone.
14. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:2, then their radius ratio will be –?
15. The number of surfaces of a solid elliptical cylinder is _____.
16. 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 height?
17. If a solid sphere is melted to form a solid right circular cylinder, then the _____ of the sphere and the cylinder are equal.
18. The English translation is: "A solid gold sphere with a radius of 4.2 cm is melted and recast into a solid right circular cylinder with a radius of 2.8 cm. Determine the height (length) of the cylinder."
19. "A hollow right circular cylinder has an external diameter of 16 cm and an internal diameter of 12 cm. Its height is 36 cm. If it is melted and recast into solid cylinders, each with a diameter of 2 cm and a height of 6 cm, calculate and write how many such solid cylinders can be made."
20. If the volumes of two right circular solid cylinders are equal and the ratio of their heights is 1:2, then find the ratio of their radii.
(a) 1:\(\sqrt2\) (b) \(\sqrt2\):1 (c) 1:2 (d) 2:1
21. The curved surface area of a solid sphere is equal to the curved surface area of a solid right circular cylinder. The height and diameter of the cylinder are both 12 cm. Write the radius of the sphere.
22. The height of a solid right circular cone is 20 cm and its slant height is 25 cm. If a solid right circular cylinder of height 15 cm has the same volume as the cone, then calculate and write the diameter of the base of the cylinder.
23. If a solid cone and a solid right circular cylinder have the same base radius and same height, and the ratio of their curved surface areas is 5:8, then determine the ratio of their base radius to height.
24. The radius of the cross-section of a solid right circular rod is 3.2 decimeters. The rod was melted and recast into 21 solid spheres, each with a radius of 4 centimeters. If so, calculate and write the length of the rod.
25. A solid right circular cone is melted and recast into a solid right circular cylinder with the same radius and a height of 5 cm. Find the height of the cone.
(a) 10 cm (b) 15 cm (c) 18 cm (d) 24cm
26. The base radius of a solid right circular cone is \(r\) units, its vertical height is \(h\) units, and its slant height is \(l\) units. The cone’s base is attached to the base of a solid right circular cylinder. If the base radius and height of the cylinder are equal to those of the cone, then the total surface area of the combined solid is \((πrl + 2πrh + 2πr^2)\) square units.
27. A solid right circular cylinder and two hemispheres have equal base radii. If the two hemispheres are attached to the flat circular ends of the cylinder, then the total surface area of the resulting solid = curved surface area of one hemisphere + curved surface area of the cylinder + curved surface area of the other hemisphere.
28. A solid sphere is melted and recast into a solid right circular cylinder. The volumes of the sphere and the cylinder are_______.
29. A solid right circular cone is melted and recast into a solid right circular cylinder. The radius of both the cone and the cylinder is the same. If the height of the cone is 15 cm, calculate and write the height of the cylinder.
30. A solid sphere has a total surface area of 1386 cm². It is melted and reshaped into several right circular cones, each with a radius of 3.5 cm and a height of 6 cm. Find the radius of the solid sphere and determine how many such cones are formed.
