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: 11


Solid cylinder of radius $1$ centered at the $ z $-axis.

Work Step by Step

Since $$ x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$ then the set $$ x^2+y^2\leq1$$ takes the form $$ r^2\cos^2\theta+r^2\sin^2\theta=r^2\leq1$$ which is a solid cylinder of radius $1$ centered at the $ z $-axis.
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