Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 8 - Section 8.5 - More Area Relationships in the Circle - Exercises - Page 378: 3


(a) $P = (12+6~\pi)~in$ (b) $A = (18~\pi)~in^2$

Work Step by Step

(a) Since the radius is $6~in$, the diameter is $12~in$ We can find the length $L$ of half the circumference: $L = \frac{1}{2}~\pi~d$ $L = \frac{1}{2}~\pi~(12~in)$ $L = (6~\pi)~in$ We can find the total perimeter of the region: $P = (12+6~\pi)~in$ (b) We can find the area of half of the full circle: $A = \frac{1}{2}~\pi~r^2$ $A = \frac{1}{2}~\pi~(6~in)^2$ $A = (18~\pi)~in^2$
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