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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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Find a formula for the area of the shaded region, which represents one-fourth of an annulus (ring).

Chapter 8.5, Problem 34E, Find a formula for the area of the shaded region, which represents one-fourth of an annulus ring.

To determine

To find:

A formula for area of shaded region.

Explanation

Formula:

Area of circle:

If r is the radius of circle, then area of circle is given by the formula:

Acircle=πr2.

Calculation:

To find the area of shaded region, let’s find the area of annulus (ring) between the two circles.

The area of ring between the two circles can be determined by subtracting the area of inner circle from the area of outer circle.

Aring=Aouter circle-Ainner circle

The radius of outer circle is R.

So, the area of outer circle = πR2

The radius of inner circle is r.

So, the area of inner circle = πr2

Aring=Aouter circle-Ainner ci

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