Question

An automobile windshield wiper 12 inches long rotates through an angle of 60°. If the rubber part of the blade covers only the last 10 inches of the wiper, find the area of the windshield cleaned by the windshield wiper.

Answer 1

`\begin{gathered} r1=12in \\ r2=10\text{ in} \\ \theta=60\text{ \degree} \\ A_s=(\pi r^2\theta)/(360) \\ A_(cleaned)=(\pi r2^2\theta)/(360)-(\pi r1^2\theta)/(360) \\ \text{Common factor} \\ A_(cleaned)=(\pi\theta)/(360)(r2^2-r1^2) \\ A_(cleaned)=(\pi(60))/(360)((12in)^2^{}-(10in)^2) \\ A_(cleaned)=(\pi(60))/(360)(144in^2^{}-100in^2) \\ A_(cleaned)=(\pi(60))/(360)(44in^2) \\ A_(cleaned)=(\pi(60))/(360)(44in^2) \\ A_(cleaned)\approx23in^2 \\ \text{The area cleaned is }23in^2 \end{gathered}`