   Chapter 9.4, Problem 28E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Given that a regular polyhedron of n faces is inscribed in a sphere of radius length 6 in., find the maximum (largest) possible volume for the polyhedron.

To determine

To find:

The maximum possible volume of a polyhedron inscribed in a sphere.

Explanation

Approach:

The surface area of a sphere S = 4πr2, where r is the radius of the sphere.

All solid bodies occupy space. The measure of occupied space is called the volume of the object, Volume of a sphere=V = 43πr3.

Calculation:

Consider the sphere of radius length 6 in.

Volume of sphere = V = 43πr3

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