Calculus: Rate of Change in Volume

Date: 07/27/97 at 14:57:24
From: Kim
Subject: Rate of change, calculus problem

Hi!  I can't figure out how to approach, much less solve the 
following.  The radius of a right circular cylinder is decreasing at 
the rate of 4 feet per minute, while the height is increasing at the 
rate of 2 feet per minute.  Find the rate of change in the volume when 
the radius is 2 feet and the height is 6 feet.

Thanks a lot for your help.

Date: 07/27/97 at 17:03:07
From: Doctor Anthony
Subject: Re: Rate of change, calculus problem

Volume of cylinder  = pi.r^2.h     dh/dt = 2,   dr/dt = -4

              dV/dt = pi[r^2.dh/dt + 2hr.dr/dt]

                    = pi[r^2(2) +2hr((-4)]

At the time when  r = 2 and h = 6 this gives

              dV/dt = pi[4 x 2 - 8 x 6 x 2]

                    = pi[8 - 96]

                    =  -88.pi     

So the volume is decreasing at the rate of 88.pi cubic feet per 
minute.

-Doctor Anthony,  The Math Forum
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