Hello. I'm having trouble with the following problem. A round hole is drilled through the center of a spherical solid of radius r. The resulting cylindrical hole has height 4 cm. What is the volume of the solid that remains? Here's the pic that I drew, I hope it's useful: http://img525.imageshack.us/img525/1954/sphereyv4.png [Broken] V of sphere = 4/3 πr^3 V of cylinder = πr^2h h = f(r) h = 4 cm I haven't really gotten anywhere yet, but the following should also be useful. I originally tried to use the shells method, the area of the rectangle of which would be A(r) = 2πr * f(r) * dr. I also noticed that as dr/dt increases dh/dt decreases. V = (4/3 πr^3) - (πr^2h) = πr^2(4/3r - 4) <--- (I'm not sure if this is useful at all but I did it anyway) I don't really know what I should do next. Any suggestions/help is greatly appreciated!