   Chapter 9.CR, Problem 25CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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:

V=e3

Where e is the each sides of the hexahedron.

Volume of Sphere:

V=43πr3

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 d=14 in.

The radius of the of the sphere is,

r=d2=142=7 in.

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 e=14 in,

Therefore, the exact volume of the space is,

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