Chapter 8.4, Problem 33E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# 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=Ï€r2.

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=Ï€R2=Ï€(r+1)2=Ï€(r2+2r+1).

Now it becomes Ao=Ï€r2+2Ï€r+Ï€

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