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: 9

Answer

The statement is false.

Work Step by Step

The volume is enclosed by the cone $z=\sqrt {x^{2}+y^{2}} $ and the plane $z=2$. If we put $z=2$ in the equation of the cone $z = \sqrt {x^{2}+y^{2}}$, we get $ x^{2}+y^{2} = 4 $. This means that the the cone intersects the plane $z=2$ in the circle $x^{2}+y^{2} = 4 $, so the volume is $$ V=\int_{0}^{2\pi} \int_{0}^{2} \int_{r}^{2} r dz dr d \theta \neq \int_{0}^{2\pi} \int_{0}^{2} \int_{r}^{2} dz dr d \theta . $$ Therefore, the statement is false.
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