Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 8 - Section 8.4 - Circumference and Area of a Circle - Exercises - Page 373: 24

Answer

(25$\pi$ - 48)$ft^{2}$

Work Step by Step

In the circle diameter of the circle = diagonal of the rectangle By pythagoras theorem $diagonal^{2}$ = $6^{2}$ + $8^{2}$ $diagonal^{2}$ = 36 + 64 diagonal = $\sqrt 100 $ = 10 ft Therefore the diameter of the circle = 10 ft Area of the circle = $\pi r^{2}$ = $\pi (5)^{2}$ = 25 $\pi ft^{2}$ Area of rectangle = 6 * 8= 48 $ft^{2}$ Therefore the shaded area = (25$\pi$ - 48)$ft^{2}$
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