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: 14


Hemisphere in the first quadrant.

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 $$ r^2\cos^2\theta+r^2\sin^2\theta+z^2=r^2+z^2= 4, \quad 0\leq\theta\leq \pi/2.$$ Which is a hemisphere in the first quadrant.
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