Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 15 - Review - True-False Quiz - Page 1118: 8

Answer

The assertion is True.

Work Step by Step

The moment of inertia about the $z$-axis of a solid $E$ with constant density $k$ is $$ \begin{aligned} I_{z}&=\iiint_{E}\left(x^{2}+y^{2}\right) \rho(x, y, z) d V \\ &=\iiint_{E}\left(k r^{2}\right) r d z d r d \theta \\ &=\iiint_{E} k r^{3} d z d r d \theta \end{aligned} $$ So the assertion is True.
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