Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 10 - Area - 10-6 Circles and Arcs - Practice and Problem-Solving Exercises - Page 655: 32

Answer

$27 \pi \ m$

Work Step by Step

Let $l$ be the length of an arc: $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times 2 \pi r ~~~(a)$ or, $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times \pi d~~(b)$ Here, $r$ represents radius and $d$ is diameter. $360^{\circ}-90^{\circ}=270^{\circ}$ and $r=18 \ m$ Thus, equation (a) becomes: $l=\dfrac{270^{\circ}}{360^{\circ}} \times 2\pi (18)=27 \pi \ m$
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