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

Step-by-step explanation

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

`A_{\text{section}}=(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(\pi)/(180º)=(8)/(9)\pi`

Now we can find the area:

`A_{\text{shaded region}}=(1)/(2)\cdot7^2\cdot(8)/(9)\pi=(196)/(9)\pi=21(7)/(9)\pi`

Answer

The area is:

`A=(196)/(9)\pi\text{ cm}^(2)`

Or expressed as a mixed number

`A=21(7)/(9)\pi\text{ cm}^(2)`