What is the area of the shaded region on which an artist can paint?

Question

An ornamental fan has a radius of 6 inches and forms a 120 degree angle when fully open. The small circular region at the base of the fan has a radius of 2 inches. What is the area of the shaded region on which an artist can paint? 

Answer 1

Sara, how do we find the area of an entire circle? Πr², right?

 

The entire circle is 360 degrees. We are finding 120/360 = 1/3 of the circle.

 

Since the entire fan has a radius of 6, then we have (1/3) Π(6²) = 12Π.

 

The area of the smaller portion is (1/3)Π(2²) = (4/3) Π.

 

Use your calculator to subtract the smaller area from the bigger area and you'll have your answer!