Chapter 9.2, Problem 39E

To determine

To find: The area that is cleared by the wiper.

Answer to Problem 39E

The area swept by the wiper is $527.78{\text{in}}^2$ .

Explanation of Solution

Given:

The angle made by wiper is $120°$ .

The length of the wiper blade is $14\text{inch}$ and the width covered by the blade is 25 inch.

Calculation:

Consider the diagram for the case is shown in Figure 1

  

Figure 1

Consider the area of the circle with the radius of 25 inch is,

  $\begin{array}{c}A=\pi {25}^2\\ =625\pi {\text{inch}}^2\end{array}$

Consider the area of the circle with radius of $\left(25-14\right)\text{in}$ is,

  $\begin{array}{c}A=\pi \left(25-14\right){\text{in}}^2\\ =121\pi {\text{inch}}^2\end{array}$

As the angle $120°$ is $\frac{1}{3}$ of the area cleared by the wiper then the area of the sector is,

  $\begin{array}{c}A=\frac{625\pi -121\pi }{3}\\ =527.78{\text{in}}^2\end{array}$