Question

What is the approximate area of a 70° sector of a circle with a radius of 8 inches?

Answer 1

`A ~~ 39.1 " inches"^2`

Explanation:

An angle of `70°` is the fraction `70/360` of the whole rotation.

A sector of a circle with a sector angle of `70°` is therefore also the fraction `70/360` of the circle

The area of the sector will therefore also be `70/360` of the area.

Sector area = `70/360 xx pi r^2`

`=7/36 xx pixx 8^2`

`A= 112/9pi`

`A ~~ 39.1 " inches"^2`
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Note that the arc length of the sector will be the same fraction of the circumference.

Arc length = `7/36 xx2pir`
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