Answer
$$ r^2=4-z^2 .$$
Work Step by Step
Since
$$ x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$
then $ x^2+y^2+z^2=4$ takes the form
$$ r^2\cos^2\theta +r^2\sin^2\theta+z^2=4\Longrightarrow r^2=4-z^2 .$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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 700: 28
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