Question

The circle has center O. Its radius is 7 cm, and the central angle a measures 160°. What is the area of the shaded region?Give the exact answer in terms of pi, and be sure to include the correct unit in your answer.

Answer 1

Explanation

The area of a section of a circle with radius 'r' and central angle 'a' in radians, is:

$A_{\text{section}}=\frac{1}{2}r^{2}a$

In this problem, the radius is 7cm and the central angle a is 160º. Since you're asked to express the result in terms of pi we have to convert this angle from degrees to radians:

$a=160º\cdot\frac{\pi}{180º}=\frac{8}{9}\pi$

Now we can find the area:

$A_{\text{shaded region}}=\frac{1}{2}\cdot7^2\cdot\frac{8}{9}\pi=\frac{196}{9}\pi=21\frac{7}{9}\pi$

Answer

The area is:

$A=\frac{196}{9}\pi\text{ cm}^{2}$

Or expressed as a mixed number

$A=21\frac{7}{9}\pi\text{ cm}^{2}$