circumscribing sphere

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.
 

Example 013
Compare the volume of a sphere inscribed in a cube with volume of the sphere that circumscribes the cube.
 

Example 012
Find the volume and total area of the sphere which circumscribes a cylinder of revolution whose altitude and diameter are each 6 inches.