Question 832030
<pre>
Hi, there--

THE PROBLEM:
A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by 
a b = 5-inch arm at the center of the base of the window, as shown in the figure below. If the arm rotates 
120°, approximate the percentage of the window's area that is wiped by the blade. (Round your answer to 
one decimal place.)

A SOLUTION:

Find the area of the rectangle window.
Let L be the length of the window.
Let W be the width.

The area is length times width, 54 * 24 = 1296 square inches.

Find the area of window swept by wipers.
The radius of the wiper is 14 inches. It wipes 120 degrees. This is one-third of a circle because 
120/360 = 1/3

The area of one-third of the circle is {{{(pi*r^2)/3=(196*pi)/3}}}

We want the percentage of the window that is swept by the wiper.

[area swept by wiper] / [area of window] * 100 = [percentage of window area swept by wiper]
{{{(((196*pi)/3)/1296)*100=15.8}}} percent.


Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com
</pre>