Can anyone help me with this math problem

I normally have no problem with math but this question doesn't make sense to me. Can anyone explain how to get the answer? Thank you.

The set of points (x,y,z) such that (x^2)+(y^2)+(z^2)=1 is

a. empty
b. a point
c. a sphere
d. a circle
e a plane

This would be a sphere of radius 1 centered at the origin.

If z=0, then you have x^2 + y^2 = 1.
If y=0, then you have x^2 + z^2 = 1.
If x=0, then you have y^2 + z^2 = 1.

So in each plane you have a circle of radius 1, so in 3 dimensions
you have a sphere of radius 1.

Hh

answer is c..a sphere