Question

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

Answer 1

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

Answer 2

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\°`

`(113.10)/(360) (cm^(2) )/(degrees)=(x)/(60) (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)`