Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.1 - Three-Dimensional Coordinate Systems - Exercises 12.1 - Page 696: 38



Work Step by Step

The whole sphere:$\quad x^{2}+y^{2}+z^{2}=1$ "Upper hemisphere" restricts the z-coordinates to $z\geq 0.$ Combined, $ x^{2}+y^{2}+z^{2}=1,\quad z\geq 0.$ Express z in terms of x and y $z^{2}=1-x^{2}-y^{2},\quad z\geq 0.$ Take the square root (result is nonnegative, so we drop the condition on z) $z=\sqrt{1-x^{2}-y^{2}}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.