Solid Geometry: Cones, Spheres, and Frustums — Engineering Board Exam Practice Questions

12 free engineering board exam reviewer questions on Solid Geometry: Cones, Spheres, and Frustums (Plane Geometry), each with the correct answer and a worked solution.

1. A sector of radius 10 and central angle 216° is rolled into a cone. Find the volume of the cone.
2. Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 6.
3. Find the total surface area of a solid hemisphere of radius 6 (curved surface plus the flat base).
4. Find the volume of a frustum of a square pyramid whose bases have sides 8 and 4 and whose height is 6.
5. Find the volume of a spherical cap of height 2 cut from a sphere of radius 6.
6. A plane cuts a sphere of radius 5 at a distance of 3 from the center. Find the area of the circle of intersection.
7. A sphere is inscribed in a cube of edge 10. Find the volume of the sphere.
8. Find the volume of a frustum of a cone with base radii 6 and 3 and a height of 4.
9. Find the lateral surface area of a right circular cone of radius 5 and height 12.
10. Find the surface area of a sphere of radius 5.
11. Find the volume of a right circular cone with radius 3 and height 4.
12. Find the volume of a sphere of radius 6.