Question

A circle has a radius of 6 inches. Find the area of a sector of this circle that is intercepted by a central angle measuring 40°.

Answer 1

We know that a central angle has it's vertex at the center of the circle and each of the sides of the angle are equal to the radius.

We know that there are 360 degrees in a circle.

We know the formula for finding the area of a circle is \[\pi r ^{2}\]
So the area of the circle is \[\pi (6^{2)}\]

So set up a proportion and solve for the area of the sector.\[40/360=x/36\pi\]