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

(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.

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