Question

What is the area of a sector MVP in terms of pi if there is a 140° and a radius of 6m?

Answer 1

The area of a sector MVP is
`14\pi \ m^(2)`

Explanation:

step 1

Find the area of the circle

The area of the circle is equal to

`A=\pi r^(2)`

we have

`r=6\ m`

substitute

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

step 2

we know that

The area of the complete circle subtends a central angle of 360 degrees

so

by proportion

Find the area of a sector for a central angle of 140 degrees

`(36 \pi)/(360) =(x)/(140)\\ \\x=36\pi *140/360\\ \\x=14\pi \ m^(2)`