Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.7 Cylindrical and Spherical Coordinates - Exercises - Page 699: 20

Answer

The set $r=2$ and $z=3$ is a disk of radius $2$ at the height of $z=3$.

Work Step by Step

In cylindrical coordinates, $r$ is always the distance back to the $z$-axis. Thus, $r=2$ corresponds to a circle of radius $2$. Since the $z$-coordinate is the same as in rectangular coordinates, $z=3$ corresponds to the plane of equation $z=3$. Hence, $r=2$ and $z=3$ is a disk of radius $2$ at the height of $z=3$.
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