Gravel is being dumped from a conveyor belt at a rate of 11 m^3/min The coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are in the ratio of 5 to 2 . How fast is the height of the pile increasing when the pile is 6 metres high?

$\displaystyle

\displaystyle v=\frac{1}{3}\pi*r^2h

$

$\displaystyle

\displaystyle v=\frac{1}{3}\pi(\frac{5}{4}h)^2h

$

$\displaystyle

\displaystyle \frac{dv}{dt}=\frac{\pi}{3}(\frac{5}{4}*h)^2+h(\fr ac{\pi}{3}*2(\frac{5}{2}*h*\frac{5}{4}*\frac{dh}{d t}))

$

$\displaystyle \displaystyle \frac{dv}{dt}=11$

$\displaystyle

\displaystyle \frac{dh}{dt}=\frac{11-\frac{\pi}{3}(\frac{5}{4}*h)^2}{\frac{11}{3}*h(\fr ac{10}{4}*h)*\frac{5}{4}}

$

When I finally plug in 6 for h, I get −.0587184655608

which appears to be wrong!

What am I doing wrong here?