regular pyramid

Problem
Determine the volume of a regular tetrahedron of edge 2 ft.

Problem
The diameter of a sphere is 18 in. Find the largest volume of regular pyramid of altitude 15 in. that can be cut from the sphere if the pyramid is (a) square, (b) pentagonal, (c) hexagonal, and (d) octagonal.
 

Example 016
Find the area of the surface and the volume of the sphere circumscribed about a regular tetrahedron of edge 25 cm. See Figure 015.
 

Regular tetrahedron is one of the regular polyhedrons. It is a triangular pyramid whose faces are all equilateral triangles.