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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

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

Chapter 9.3, Problem 35E, In Exercises 34 and 35, give a paragraph proof for each claim. The volume V of a washer that has an

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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