Probability / 3D Geometry Problem

Question

A point in space $(x,y,z)$ is randomly selected so that $-1\le x \le 1$,$-1\le y \le 1$,$-1\le z \le 1$. What is the probability that $x^2+y^2+z^2\le 1$?

Answer 1

Let $A=\{(x,y,z):x^{2}+y^{2}+z^{2}\leq 1\}$ and let $B=\{(x,y,z):-1\leq x,y,z\leq 1\}$. Since $A\subset B$, the probability that the point will be in $A$ is $$ \frac{\operatorname{Volume}(A)}{\operatorname{Volume}(B)}. $$

I guess you can take it from here.