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

Answer:

$27\pi \ cm^{2}$

Step-by-step 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 $270\°$

$\frac{36 \pi}{360} \frac{\ cm^{2}}{degrees}=\frac{x}{270} \frac{\ cm^{2}}{degrees} \\ \\ x=270*36\pi /360\\ \\x=27\pi \ cm^{2}$