   Chapter 9.3, Problem 35E 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

In Exercises 34 and 35, give a paragraph proof for each claim.The volume V of a washer that has an inside radius of length r , an outside radius of length R , and an altitude of measure h is given by V = π h ( R + r ) ( R − r ) . To determine

To give:

The paragraph proof for the claim “The volume V of a washer that has an inside radius of length r, an outside radius of length R, and an altitude of measure h is given by V=πh(R+r)(Rr)”.

Explanation

Given:

The claim is “The volume V of a washer that has an inside radius of length r, an outside radius of length R, and an altitude of measure h is given by V=πh(R+r)(Rr)”.

Proof:

Consider a circular cylinder.

Let r be the inside radius, R be the outside radius and h be the altitude of the circular cylinder.

The volume of the circular cylinder with radius r is V1=πr2h

The volume of the circular cylinder with radius R is V2=πR2h

Hence the volume of the washer is V=V2V1

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