   Chapter 9.CR, Problem 23CR 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

Find the exact volume of the solid of revolution that results when a semicircular region with diameter of length 4 in. is rotated about that diameter.

To determine

To find:

The volume of the solid of revolution.

Explanation

Formula used:

Volume of sphere:

V=43πr3

Given:

The exact volume of the solid of revolution that results when a semicircular region with diameter of length 4 in. It is rotated about that diameter.

Calculation:

The solid of revolution that results when a semicircular region as shown in the figure,

The solid of revolution that results when a semicircular region, it is form a sphere.

So, we find the volume of the sphere,

The diameter of the half sphere is d=4 in.

The diameter of the half sphere is,

r=d2=42r=2 in

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