Find the area of the sector of a circle with radius 4 inches formed by a central angle of (5\pi)/(4) radians. Give your answer correct to 3 decimal places.

Question

Find the area of the sector of a circle with radius 4 inches formed by a central angle of
`(5\pi)/(4)` radians. Give your answer correct to 3 decimal places.

Answer 1

10in²

Explanation:

5π/4 is 62.5% of a circle if you look at the unit circle.

So just find the area of a circle and take 62.5% of it.

A = πr²

A = π(4)²

A = 16π

16π(.625) = 10