Hey guys, I want to make sure I am on the right track with this problem: The radius of a sphere is increasing at a rate of 4 cm/s. How fast is the volume increasing when the radius is 40 cm? (Recall the formula relating the area A and radius r of a sphere: A = 4πr^2.) So, I use the equation A=4πr^2 I take the derivate with respect to time. dA/dt = 4π*2r*dr/dt Simplifying : dA/dt = 8π*r*dr/dt Inputing radius of 40cm for variable r and inputting rate of 4cm/s for variable "dr/dt" The answer becomes dA/dt = 1280π cm^2/sec The answer seems to make sense (units). This just seems too... easy for me. In class we were doing a bit more difficult problems. Does everything check out? Thanks.