You don't need to integrate anything.

First we want the volume of a sphere, which is:

We are tasked with finding a rate of change, which means we are going to be dealing with derivatives.

We are told that is equal to "10 cubic feet per second". We need to find .

Taking the derivative of the volume of a sphere, and differentiating it with respect to time, will yield us an equation, that we can solve for .

If you need further help lemme know.