The surface area of a sphere is given by
[tex]S = 4\pi r^2[/tex]
We deduce
[tex]r = \sqrt{\dfrac{S}{4\pi}}[/tex]
So, in your case, the radius is
[tex]r = \sqrt{\dfrac{100\pi}{4\pi}}=\sqrt{25}=5[/tex]
The volume of a sphere is given by
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
So, we have
[tex]V = \dfrac{4}{3} \pi 5^3 = \dfrac{500}{3}\pi[/tex]
