The diameter of a circle is 16 meters. What is the angle measure of an arc bounding a sector with an area eight pi square meters? (give the exact answer in simplest form)

Answer: 45°

Step-by-step explanation:

Diameter = 16m

Radius = 16/2 = 8m

The area of the circle = πr^2

= π8^2

= 64π square metres.

An area of 8π square metres is also 1/8 of the total area, therefore the arc must be 1/8 of the circumference.

The circumference = 2πr = 16π,

This gives us an arc length of 2π metres.

But since we are looking for the the angle.

In degrees: 360/8 = 45°