1. The number of surfaces in a solid hemisphere is _____.
2. "The number of plane surfaces of a solid hemisphere is ______________."
3. The number of surfaces of a solid right circular cylinder is _____.
4. The number of surfaces of a solid right circular cylinder is _____.
5. The number of surfaces of a solid right circular cylinder is 3.
6. The number of surfaces of a solid elliptical cylinder is _____.
7. Two identical solid hemispheres, each with a base radius of \(r\) units, are joined together along their flat surfaces. The total surface area of the resulting solid body will be \(6πr^3\) square units.
8. The volume of the largest solid cone that can be cut out from a solid hemisphere with a radius of r units.
(a) \(4\pi r^3\) cubic units. (b) \(43\pi r^3\) cubic units. (c) \(\cfrac{πr^3}{4} \) cubic units (d) \(\cfrac{πr^3}{3}\) cubic units
9. The numerical value of the volume and the total surface area of a solid hemisphere are equal. Find the radius of the hemisphere.
10. The total surface area of a solid hemisphere and the curved surface area of a solid sphere are equal. What is the ratio of the radius of the hemisphere to the radius of the sphere?
11. A solid hemisphere and a solid cone have the same base radius and height. What is the ratio of their volumes?
(a) 3:2 (b) 1:3 (c) 2:3 (d) None of the above
12. If the volume of a solid hemisphere is \(144π\) cubic centimeters, what is the diameter of the sphere?
13. The total surface area and volume of a solid hemisphere are numerically equal. Find the radius of the base of the hemisphere.
14. If a solid hemisphere and a solid cone have the same base radius and height, what is the ratio of their volumes?
15. If a solid hemisphere and a solid cone have equal base diameters and equal heights, find the ratio of their curved surface areas.
16. Determine the volume ratio of a solid cone, a solid hemisphere, and a solid cylinder with equal base diameters and equal heights.
17. A solid hemisphere and a solid cone have the same base radius and height. Determine the ratio of their volumes.
(a) 3:2 (b) 11:3 (c) 2:3 (d) 4:3
18. If a solid hemisphere has a radius of \(2r\) units, then its total surface area is ____ \(\pi r^2\) square units.
19. A solid hemisphere and a solid cone have the same base diameter and height. Determine the ratio of their volumes and the ratio of their curved surface areas.
20. If the radius of a solid hemisphere is \(3r\) units, then its total surface area is _____.
21. The ratio of the total surface area to the curved surface area of a solid hemisphere will be –.
(a) 2:1 (b) 1:2 (c) 1:3 (d) 3:1
22. If the volume of a solid hemisphere is \(144\pi\) cubic cm, what is its total surface area?
23. Determine the volume of the largest solid cone that can be cut from a solid hemisphere with a radius of \(r\) units.
24. The ratio of the curved surface area to the total surface area of a solid hemisphere is _____.
25. 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.
26. If a solid hemisphere is melted to form a sphere, what will be the ratio of their radii?
27. The curved surface area and the total surface area of a solid hemisphere are equal.
28. If the curved surface area of a solid hemisphere is \( S \) and its volume is \( V \), find the value of \( \cfrac{S^3}{V^2} \).
29. If the composite mean of the numbers in the following frequency distribution table is 24, determine the value of \( p \).
30. A solid object has its lower part in the shape of a hemisphere and its upper part in the shape of a right circular cone. If the surface areas of both parts are equal, determine the ratio of the radius to the height of the cone.
