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 solid right circular cylinder is 3.
4. The number of surfaces of a right circular cylinder is _____.
5. The number of surfaces in a solid hemisphere is _____.
6. "The number of plane surfaces of a solid hemisphere is ______________."
7. The number of surfaces of a solid hemisphere is ——.
8. A solid sphere is melted to form a solid vertical cylindrical rod. The volume of the sphere and the cylinder is _____.
9. A solid sphere is melted and recast into a solid right circular cylinder. The volumes of the sphere and the cylinder are_______.
10. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be –
(a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9
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. 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.
13. If a solid sphere is melted to form a solid right circular cylinder, then the _____ of the sphere and the cylinder will be equal.
14. A hollow iron cylinder of height 20 cm has an outer radius of 5 cm and an inner radius of 4 cm. This cylinder is melted and recast into a solid cone whose height is one-third of the original cylinder's height. Find the diameter of the base of the cone.
15. 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?
16. The number of real roots of the equation \((x - 1)^2 + (x - 2)^2 + (x - 3)^2 = 0\) is ______.
17. If the product of three consecutive positive geometric numbers is 64, then the mean proportional between the first and the third is ______.
18. 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
19. Determine the volume ratio of a solid cone, a solid hemisphere, and a solid cylinder with equal base diameters and equal heights.
20. If the product of three consecutive positive numbers in geometric progression is 64, then their geometric mean is _____.
21. If the radius of a solid hemisphere is \(3r\) units, then its total surface area is _____.
22. The total number of vertices of a cube is _____.
23. If a rectangular prism has the number of faces \(= x\), the number of edges \(= y\), and the number of vertices \(= z\), then \(z - \cfrac{y}{x} =\) _____.
24. A hollow cylinder with a height of 13 cm has an outer radius of 6.75 cm and an inner radius of 5.25 cm. It is melted to form a solid cylinder with a height of 6.5 cm. Find the radius of the solid cylinder.
25. 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) \(1:\sqrt2\)
26. The ratio of the curved surface area to the total surface area of a solid hemisphere is _____.
27. 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.
28. 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.
29. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:2, then their radius ratio will be –?
30. If the length, width, and height of a right rectangular prism are equal, then the special name for that solid object is _____.
