   Chapter 8.5, Problem 6E 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

If the area of the circle is 360 in2, what is the area of the sector if its central angle measures 900? To determine

To find:

The area of shaded sector.

Explanation

Definition:

Arc Measure:

In a circle, the degree measure of an arc is equal to the measure of central angle that intercepts the arc.

Formula:

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 measure of central angle is given as 900.

As per the definition of measure of an arc, the degree measure of an arc is equal to the central angle intercepted by it.

Thus, the degree measure of arc AB^ = 900. Hence, m=900

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

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