# Math Help - Related Rates problem

1. ## Related Rates problem

I don't understand this problem at all. Can someone please help me break it down? I would post my work if I even knew how to start it but I don't.

Sand falls from a conveyor belt onto the top of a conical pile at a constant rate of 15 m^3/min. The height of the pile is always 3/5 of the base diameter. How fast is the height changing when the pile is 3 m high? At the same instant, how fast is the base radius changing?

2. $V = \frac{\pi}{3} r^2 h$

$h = \frac{3}{5}d = \frac{3}{5}(2r) = \frac{6}{5}r$

sub the last expression for $h$ to get the volume formula strictly in terms of the variable $r$.

take the time derivative.

solve for $\frac{dr}{dt}$.

take the time derivative of $h = \frac{6}{5}r$ and calculate $\frac{dh}{dt}$.