Area of a windshield wiper

Question

The windshield of a car has a total length of arm and blade of

11 ​inches, and rotates back and forth through an angle of

93degrees°. What is the area of the portion of the windshield cleaned by the

9​-in wiper​ blade?

Answer 1

First, draw a circle with a radius of 11 inches (Maybe scale by a factor of 2-3 to fit the paper). The area of this circle is pi * 11^2 (A = pi*r^2)

The is an inner circle that is not swept by the wiper blade--that has a radius of 2 inches (11 -9), so it's area is pi * 2^2. Subtract this from the larger circle.

So A for the full circle = A(FC) = pi * (11^2 - 2^2)

Finally, find the portion that is covered by the 93 degree angle. A full circle is 360 degrees so the swept area is A(FC) * 93/360