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: 31

Answer

Area of Ring = Area of outer circle - Area of inner circle the area of the ring = $\pi R^{2}$ - $\pi r^{2}$ = $\pi (R^{2} -r^{2})$ As we know $ (a^{2} -b^{2})$ = (a+b)(a-b) Area of the Ring =$\pi$(R+r)(R-r)

Work Step by Step

Given concentric circles with radii of lengths R and r where R > r We need to explain why A = $\pi$(R+r)(R-r) The area A of a circle whose radius has length r is given by A = $\pi r^{2}$ The area of the outer circle = $\pi R^{2}$ The area of the inner circle = $\pi r^{2}$ the area of the ring = $\pi R^{2}$ - $\pi r^{2}$ = $\pi (R^{2} -r^{2})$ As we know $ (a^{2} -b^{2})$ = (a+b)(a-b) therefore A=$\pi$(R+r)(R-r)
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