# Math Help - sand problem

1. ## sand problem

ok sand pouring from a chute forms a conical pile whose height is always equal to the diameter. if the height increases at a constant rate of 5 ft/min, at what rate is sand pouring from the chute when the pile is 10ft high? thanks in advance.

2. Originally Posted by slapmaxwell1
ok sand pouring from a chute forms a conical pile whose height is always equal to the diameter. if the height increases at a constant rate of 5 ft/min, at what rate is sand pouring from the chute when the pile is 10ft high? thanks in advance.
$V = \frac{\pi}{3} r^2 h$

since $h = 2r$ ... $r = \frac{h}{2}$

$V = \frac{\pi}{3} \left(\frac{h}{2}\right)^2 h$

simplify the formula for V in terms of h , then take the derivative w/r to time.

you were given $\frac{dh}{dt} = 5$ ft/min ... calculate $\frac{dV}{dt}$ when h = 10 ft