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 700: 57

Answer

Please see the figure attached.

Work Step by Step

In spherical coordinates, $\rho$ is the distance back to the origin. Thus, $\rho=2$ describes a sphere of radius $2$. Now, $\theta$ is the polar angle of the projection $Q$ of a point $P$ on the sphere onto the $xy$-plane. Since it is constant $\theta = \frac{\pi }{4}$, the sphere reduces to a circle of radius $2$.
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