regular pyramid

Volume of pyramid cut from a 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.
 

016 Radius of the sphere circumscribing a regular triangular pyramid

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.
 

Sphere circumscribed about a regular tetrahedron

 

The Regular Tetrahedron

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

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