   Chapter 8.5, Problem 25E 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

Assuming that the exact area of a sector determined by a 40 0 arc is 9 4 π cm2, find the length of the radius of the circle.

To determine

To find:

The length of radius of the circle.

Explanation

Formula:

Area of sector:

If r is the radius of the circle, the area A of a sector whose arc has degree measure m is given by

A=m360×πr2

Calculation:

The degree measure of arc is 400. Hence, m=400

The formula for area A of sector is:A=m360×πr2.

The area of sector is given as 94π cm2. Hence, A=94π cm2

Let’s substitute the value of A and m to find the length of radius of circle.

94π=40360×π×r2

Simplify:94π=19×π×r

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