Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.10 - Modeling with Functions - Exercise Set - Page 296: 65



Work Step by Step

Step 1. Using the figure given in the exercise, the perimeter can be expressed as $\pi r+2r+2h=12$ which gives $h=6-r-\frac{\pi}{2}r$ Step 2. The area of the window is given by $A=\frac{\pi}{2}r^2+2rh=\frac{\pi}{2}r^2+2r(6-r-\frac{\pi}{2}r)=\frac{\pi}{2}r^2+12r-2r^2-\pi r^2=12r-(2+\frac{\pi}{2})r^2$
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