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 656: 56

Answer

$18 \ cm$

Work Step by Step

$l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times 2 \pi r ~~~(a)$ or, $l=\dfrac{\text{Measure of the arc}}{360^{\circ}} \times \pi d~~(b)$ Here, $r$ represents radius and $d$ is diameter. Thus, equation (b) becomes: Length $\widehat{AB}=\dfrac{m \widehat{AB}}{360^{\circ}} \times \pi d$ or, $6\pi=\dfrac{120^{\circ}}{360^{\circ}} \times \pi d$ or, $d=18 \ cm$
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