   Chapter 8.4, Problem 31E 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

Given concentric circles with radii of lengths R and r, where R > r , explain why A r i n g = π ( r + r ) ( R − r ) . To determine

To explain:

Aring=π(R+r)(Rr), for concentric circles with the radii of lengths R and r.

Explanation

Two circles with a common center are called concentric circles.

A region bounded by two concentric circles is called ring.

Calculation:

The length of the radius of the outer circle is R.

The area of the outer circle is πR2.

Next, the length of the radius of the inner circle is r.

The area of the inner circle is πr2.

Now to find the area of the ring, subtract the area of the inner circle from the area of the outer circle.

Therefore, Aring=πR2πr2

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