In circle O the area of the sector with central angle AOB is 30 pi cm squared and radius OA is 6 cm. What is the angle measure of arc AB and the length of AB?

The area of the whole circle is PI x 6 squared which equals 36 PI.

We can now use the ratio 30/36 = x/360 to find the angle (360 is the full angle if the circle, x is the angle of the segment, pi's cancell out)

If we solve for x we get 300 degrees which is the angle we need.

As for the length, the circles circumference is 12 PI (12 is the diameter).

This means that 30/36= AB/12PI

AB=10PI