   Chapter 9.3, Problem 34E 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 total area T of a right circular cylinder whose altitude is of length h and whose circular bas has a radius of length r is given by T = 2 π r ( r + h ) . To determine

To give:

The paragraph proof for the claim “The total area T of a right circular cylinder whose altitude is of length h and whose circular base has a radius of length r is given by T=2πr(r+h)”.

Explanation

Given:

The claim is “The total area T of a right circular cylinder whose altitude is of length h and whose circular base has a radius of length r is given by T=2πr(r+h)”.

Proof:

Consider a right circular cylinder.

Let r be the radius of the base of the cylinder and h be the altitude of the cylinder.

The lateral area of the right circular cylinder is L=2πrh.

The base of the cylinder is a circle with radius r.

The base area of the right circular cylinder is B=πr2.

Hence the total area of the right circular cylinder is T=L+B

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