Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 12 - Section 12.1 - Three-Dimensional Coordinate Systems - 12.1 Exercises - Page 797: 40


$x^2+y^2 \leq 4$ and $0\leq z \leq 8$

Work Step by Step

"A solid cylinder...with center at the origin and radius 2" : $x^2+y^2 \leq 2^2$ or $y^2+z^2 \leq 2^2$ or $x^2+z^2 \leq 2^2$ "lies on or below z= 8": $z\leq 8$ and on or above the disk in the xy-plane: $z \geq 0$ and $x^2+y^2 \leq 2^2$ Combine these rules to find: $x^2+y^2 \leq 4$ and $0\leq z \leq 8$
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