   Chapter 8.4, Problem 33E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# The radii of two concentric circles differ in length by exactly 1 in. If their areas differ by exactly 7π in2, find the lengths of the radii of the two circles.

To determine

To Find:

The lengths of radii of two concentric circles.

Explanation

Two circles with a common center are called concentric circles.

Calculation:

Let the length of the radius of the inner circle is r and the area is Ai and the length of the radius of the outer circle is R and the area is Ao.

The area of the inner circle is Ai=πr2.

The length of the radius of the outer circle is 1 in higher than the inner circle.

Therefore, the radius of the outer circle is R=r+1.

The area of the outer circle is.

Ao=πR2=π(r+1)2=π(r2+2r+1).

Now it becomes Ao=πr2+2πr+π

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