Spherical Tank Filling / Related Rates Problem
This is straight out of a Calc 1 text, and I am having trouble figuring it out. I'm assuming I shouldn't have to integrate, since it's from calc 1.
"Water is being pumped into a spherical tank of radius 60 feet at the constant rate of 10 cubic feet per second. Find the rate at which the radius of the top level of water in the tank changes when the tank is half full."
It should be 0, since that's where the radius will begin to shrink again, but I can't prove it mathematically.