Question

A car's rear windshield wiper rotates 130°. the total length of the wiper mechanism is 21 inches and the length of the wiper blade is 14 inches. find the area wiped by the wiper blade. (round your answer to one decimal place.)

Answer 1

We have that the formula for the area of the sector of a circle is:

`A=(\pi\cdot r^2\cdot\alpha)/(360)`

In this case, we have to find the area of the sector of a circle with radius r= 21 and then the area in the case of the r=21-14=7, and then find the difference.

Given the information, we have the following:

`\begin{gathered} \alpha=130 \\ r_1=21 \\ r_2=7 \\ \Rightarrow A_1=((3.1416)(21)^2(130))/(360)=500.3 \\ \Rightarrow A_2=((3.1416)(7)^2(130))/(360)=55.6_{} \\ \Rightarrow A=A_1-A_2=500.3-55.6=444.7_{} \\ A=444.7 \end{gathered}`

therefore, the area wiped by the wiper blade is 444.7in²