Let R=13 ft be the radius of the spherical tank, h be the depth of the water in the tank, and r be the radius of the (circular) surface of the water. Drawing a vertical cross-section of the tank, we see that the distance from the surface to the center of the sphere is R-h, and that a radius r of the surface and the center of the sphere form a right triangle with legs R-h, r, and hypoteneuse R

Thus

We find using the chain rule:

We know is -2 ft/hr, so we can obtain in ft/hr as a function of h from the above. Then just put in R=13 ft and h=8 ft to get the answer.

--Kevin C.