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: 30

Answer

4:1

Work Step by Step

The ratio of the circumferences of two circles is 2:1. We need to find the ratio of their areas Let us assume the circle radius of the first one is r1 and the second one is r2 The circumference ratios is 2$\pi$r1 : 2$\pi$r2 = 2:1 r1 : r2 = 2:1 Let us assume r1 = 2x and r2 = x The area A of a circle whose radius has length r is given by A = $\pi r^{2}$ Therefore A1 : A2 = $\pi r1^{2}$ :$\pi r2^{2}$ $r1^{2}$ : $r2^{2}$ $(2x)^{2}$ : $(x)^{2}$ 4$x^{2}$ : $(x)^{2}$ A1:A2 = 4:1
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