Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.7 Polynomials in Several Variables - 4.7 Exercise Set - Page 285: 95


$$2\pi ab-\pi b^2$$

Work Step by Step

We know the following equation for the area of the shaded region: $$ A_{shaded}=\text{Overall Area} - \text{ Area Used Up}$$ Using this, we find: $$ \pi a^2 - \pi (a-b)^2 \\ \pi a^2-\pi \left(a^2-2ab+b^2\right) \\ 2\pi ab-\pi b^2$$
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