Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 8 - Section 8.4 - Circumference and Area of a Circle - Exercises - Page 384: 23

Answer

(32$\pi$ - 64)$in^{2}$

Work Step by Step

In the circle diameter of the circle = diagonal of the square By pythagoras theorem $diagonal^{2}$ = $8^{2}$ + $8^{2}$ $diagonal^{2}$ = 64 + 64 diagonal = $\sqrt 128 $ = 8$\sqrt 2$ in Therefore the diameter of the circle = 8$\sqrt 2$ in Area of the circle = $\pi r^{2}$ = $\pi (4\sqrt 2)^{2}$ = 32$\pi in^{2}$ Area of square = $s^{2}$ = $8^{2}$ = 64 $in^{2}$ Therefore the shaded area = (32$\pi$ - 64)$in^{2}$
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