Chapter 8.5, Problem 7E

### 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

# If the area of 1200 sector is 50 cm2, what is the area of the entire circle?

To determine

To find:

The area of entire circle.

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=m360Ã—Ï€r2

Calculation:

The measure of central angle is given as 1200.

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^ = 1200. Hence, m=1200

The formula for area A of sector is:A=m360Ã—Ï€r2.

Area A of sector is given as 50 cm2

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