A cylinder is of 0.08 foot thickness and when the radius is 150 feet, the radius is increasing at the rate of 0.5 foot per minute.It's asking for the rate in cubic feet per minute.

I decided to derive the formula for a cylinder, which is $\displaystyle pi*r^2*h = y$ and got;

$\displaystyle dy/dt = 2*pi*r*dr/dt*dh/dt$

$\displaystyle dy/dt = 2*pi*150*0.5*0.08$

$\displaystyle dy/dt = 12pi$ ... which isn't the answer. (~37.7 ft^3/min)

What did I do wrong?