Question

A 20° sector in a circle has an area of 21.5π yd². What is the area of the circle? Use 3.14 for pi.

Answer 1

This would be 21.5π * 360 / 20 yd^2  =  1215.18 yd^2 ( using pi = 3.14)

Answer 2

The area of the circle is
`1,215.18\ yd^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

`360\°` subtends the complete circle of area
`\pi r^(2)`

so

by proportion

Find the area of the complete circle if a
`20\°` sector has an area of
`21.5\pi\ yd^(2)`

`(x)/(360)=(21.5\pi)/(20)\\ \\x=360*21.5\pi /20\\ \\x=387\pi \ yd^(2)`

`387\pi \ yd^(2)=387*3.14=1,215.18\ yd^(2)`