how do I find the radius of a sphere when the only thing that's given to you is surface area?

Area of a sphere

A = 4 pi r^2

solve for r

r= SQRT ( A/(4 pi))

The Surface Area =   4 * pi * r^2

So...in your case, we have

84.5 = 4 * pi * r^2       divide both sides by 4pi

84.5 / [4pi]   = r^2     take the square root of both sides

2.593 in ≈  r

\(\mbox{the surface area is } n. \sqrt{\frac{n}{4\pi}}= \mbox{the radius.}\)