Using the first question in the webpage: http://www.math.ubc.ca/~lior/teaching/1213/100_F12/Quiz/100_Quiz07_soln.pdf   Why isn't the function Pi*R^2*h differentiated as 2*Pi*r*h' ?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We are given a cylindrical tank with radius of 5m. The tank is being filled at a rate of 3 cubic meters per minute, and we are asked to find the rate of change of the height of the water.

The volume at time t is `V(t)=pir^2h(t)` so `(dV)/(dt)=(pir^2)h'(t)` since r is a constant.

The solver could just have easily have used `V=25pih` so `(dV)/(dt)=25pih'(t)` . Why didn't they? The method used can now be generalized to right cylindrical tanks of any given radius -- just substitute the given radius for r.

Approved by eNotes Editorial Team