Find the area of the shaded sector of the circle. Leave your answer in terms of \pi

Question

Find the area of the shaded sector of the circle. Leave your answer in terms of
`\pi`

Answer 1

The area of a circular sector is proportional to the central angle that it encloses.

Since the non-shaded region encloses an angle of 200°, then the shaded region must enclose an angle of 160°, so that 200+160=360.

Multiply the area of a complete circle by 160/360 to find the area of the shaded sector.

The area of a circle is given by:

`A=\pi r^2`

Then, the area of a circular sector that encloses an angle k measured in degrees, is:

`A=\pi r^2\cdot(k)/(360)`

In the given diagram, we can see that the radius equals 9yd. Then, the area of the shaded sector is:

`\begin{gathered} A=\pi(9yd)^2\cdot(160)/(360) \\ =\pi\cdot81\cdot(4)/(9)yd^2 \\ =36\pi yd^2 \end{gathered}`

Therefore, the area of the shaded sector is:

`36\pi yd^2`