The total arm and blade of a single windshield wiper was 10 in. long and rotated back and forth through an angle of 95°. A portion of the windshield is cleaned by 7-in. wiper blade. What is the area of the region cleaned?
Area of a sector = 1/2 r2θ
The Attempt at a Solution
My first guess was to simply calculate the area cleaned by the blade and I thought that would be my answer.
In the book though, they calculated the area not cleaned by the blade (r would be equal to (10-7)2) and subtracted it from the total area. I can't wrap my head around that. Why subtract the two areas? Why not just calculate the area that was cleaned by the blade? My guess is it has something to do with the actual angle or radius, but I'd like a little clarification to make sure I really understand this. Thanks!