Chapter 4, Problem 104RE

Solution

To find: How large area does the blade clean

  $A=614.36i{n}^2$

Given information: the centre of blade is usually attached to the end of the windshield wiper arm, so the total length of the windshield wiper is $20+\frac{1}{2}(16)=28in$ .

Draw the situation as shown below with required area in blue

  

Formula used: Trigonometry

Calculation: The shaded area is the difference of the two sectors, so we will use the formula:

  $A=\frac{1}{2}{r}^2\theta$

Where r is the radius and theta is the radians.

The larger sector has a radius of 28in and the smaller sector has a radius of $12$ in. both have $\begin{array}{c}\theta ={110}^{\circ }\times \frac{\pi }{{180}^{\circ }}\\ =\frac{11\pi }{18}\end{array}$

Now we have:

  $\begin{array}{l}$ A=\frac{1}{2}{(28)}^2\cdot \frac{11\pi }{18}-\frac{1}{2}{(12)}^2\cdot \frac{11\pi }{18}$A\approx 614.36i{n}^2\end{array}$