Question

The circle has center O. Its radius is 3 m, and the central angle a measures 60°. 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 portion of a circle with radius 'r' and angle 'a' (in radians) is:

`A_{\text{portion}}=(1)/(2)\cdot r^2\cdot a`

In this problem r = 3m, a = 60º.

First we have to express the angle in radians:

`a=60º\cdot(\pi)/(180º)=(1)/(3)\pi`

The area of the shaded region is:

`\begin{gathered} A=(1)/(2)\cdot(3m)^2\cdot(1)/(3)\pi \\ A=(1)/(2)\cdot9m^2\cdot(1)/(3)\pi=(3)/(2)\pi \end{gathered}`

Answer

The area is:

`A=(3)/(2)\pi`