Question

What is the approximate area of the shaded sector in the circle shown below? 

Answer 1

we know that

The area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

In this problem we have

$r=6\ cm$

Substitute the value of r in the formula

$A=\pi (6^{2})=113.10\ cm^{2}$

Remember that

The area of $113.10\ cm^{2}$ subtends the complete circle of $360\°$

so

by proportion

Find the area for the shaded sector of $60\°$

$\frac{113.10}{360} \frac{cm^{2} }{degrees}=\frac{x}{60} \frac{cm^{2} }{degrees} \\ \\x=60*113.10/360 \\ \\x= 18.85\ cm^{2}$

therefore

The answer is

The approximate area of the shaded sector is $18.85\ cm^{2}$

Answer 2

(60/360)(pi)(36)= 6pi or 18.84