Calculating the volume of a spherical cap.

I'm not sure this is in the right section, as it's not a school problem as such, but a problem given to me by a stuck friend. So forgive me if it's in the wrong area.

Anyways:

If you put a perfect sphere into a tub of water, it displaces 280,000 cubic centimetres of water. 72% of the surface area of the sphere is below the water. Calculate the total volume of the sphere.

Appears simple at first, but it's not, and I have no idea where to go with the calculations. A solution would be much appreciated :)