College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 1 - Conceptual Questions: 4

Answer

(a) If we triple the radius, then the circumference increases by a factor of 3. (b) If we triple the radius, then the area increases by a factor of 9.

Work Step by Step

(a) Let $r$ be the original radius of the circle. The circumference is $C_1 = 2\pi r$ If we triple the radius, then the new radius is $3r$ The new circumference is $C_2 = 2\pi (3r) = 3\times 2\pi r = 3\times C_1$ If we triple the radius, then the circumference increases by a factor of 3. (b) Let $r$ be the original radius of the circle. The area is $A_1 = \pi r^2$ If we triple the radius, then the new radius is $3r$ The new area is $A_2 = \pi (3r)^2 = 9\times \pi r^2 = 9\times A_1$ If we triple the radius, then the area increases by a factor of 9.
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