finding rate of change

Question

The volume of a cylinder is increasing at a rate of 248in^3/min . Suppose that the height is increasing at 10 in/min. Find the rate of change of the radius at the instant when the volume is 1000 in3 and the radius is 12 in. Note the volume formula for a cylinder is V=pir^2

Answer 1

So formula for a cylinder is 

V = (pi*r^2)*h

take the derivative with respect to time, t. Use the product rule and implicit differentiation and you have 

 

dV/dt = (2pi*r*dr/dt)*h + (pi*r^2)*dh/dt

 

you are given dV/dt, dh/dt, V, r. From this you can get h using formula for volume of cylinder 

h = V/(pi*r^2)

you can now solve for dr/dt using formula above

 

best - david