Chapter 9.CR, Problem 25CR

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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A sphere with a diameter length of 14 in. is inscribed in a regular hexahedron. Find the exact volume of the space inside the hexahedron but outside the sphere.

To determine

**To find:**

The exact volume of the space.

Explanation

**Formula used:**

Volume of Hexahedron:

Where

Volume of Sphere:

**Given:**

A sphere with a diameter length of 14 in. is inscribed in a regular hexahedron. Find the exact volume of the space inside the hexahedron but outside the sphere.

**Calculation:**

The diameter of the sphere is

The radius of the of the sphere is,

A sphere with a diameter length of 14 in. is inscribed in a regular hexahedron, so the diameter of length is equal to the hexahedron each sides of the length.

That is the length of the each sides of the of the hexahedron is

Therefore, the exact volume of the space is,

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