Hi there!
We can find the surface of a sphere by using the following formula:
[tex]surface \: = 4\pi {r}^{2} [/tex]
In this formula r represents the radius of the sphere. We don't already know this radius, but we do know the surface area of the sphere. By substituting this area into the formula, we can set up an equation.
[tex]100\pi = 4\pi {r}^{2} [/tex]
First divide both sides by 4 pi.
[tex] \frac{100\pi}{4\pi} = \frac{4\pi {r}^{2} }{4\pi} [/tex]
Some algebra
[tex]25 = r {}^{2} [/tex]
Now take the root of both sides. In this case we only need the positive solution, because a radius (and a length) cannot be negative.
[tex]r = \sqrt{25} = 5[/tex]
Therefore, the radius of the sphere is 5 cm.
~ Hope this helps you!
