Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 482: 41

Answer

(a) The sphere has symmetry with respect to the x-axis. (b) The sphere has symmetry with respect to the xy plane.

Work Step by Step

We can write the general equation of a sphere: $(x-a)^2+(y-b)^2+(z-c)^2 = r^2$ where $(a,b,c)$ is the center of the sphere and $r$ is the radius The equation of the sphere is: $x^2+y^2+z^2 = 100$ The center of the sphere is $(0,0,0)$ (a) The x-axis is a line. A sphere has symmetry with respect to any line that passes through the sphere's center. Since the x-axis passes through the point $(0,0,0)$, the sphere has symmetry with respect to the x-axis. (b) A sphere has symmetry with respect to any plane that includes the sphere's center. Since the xy plane includes the point $(0,0,0)$, the sphere has symmetry with respect to the xy plane.
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.