Question

Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer 1

a full circle has a measure of 360 degree. the graph shows a 3/4 circle.
3/4 of π*6²=27π
27π is the answer.

Answer 2

`27\pi \ cm^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

we have

`r=6\ cm`

substitute

`A=\pi (6)^(2)=36 \pi\ cm^(2)`

Remember that a central angle of
`360\°` subtends for the area of a complete circle

so

by proportion

Find the area of the circle for a central angle of
`270\°`

`(36 \pi)/(360) (\ cm^(2))/(degrees)=(x)/(270) (\ cm^(2))/(degrees) \\ \\ x=270*36\pi /360\\ \\x=27\pi \ cm^(2)`