Describe the set of points for the given inequality. $x^2+y^2+z^2=36$, and $x^2+y^2+z^2\geq 36$

Question

To describe $x^2+y^2+z^2=36$, I know this is not a circle, so we can't say the origin is 36. Instead would it be correct to say, with what we know we can find the center and the radius of the sphere?

For $x^2+y^2+z^2\geq 36$ I have the same idea, but I'm not sure what this means with the inequality.

Answer 1

This just means $||(x,y,z)|| = 6$ and $||(x,y,z)||\geqslant 6$ so you are looking at the sphere of radius $6$ and its exterior in $\mathbb{R}^3$.