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.
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.
$\displaystyle V = \frac{\pi}{3} r^2 h$
since $\displaystyle h = 2r$ ... $\displaystyle r = \frac{h}{2}$
$\displaystyle V = \frac{\pi}{3} \left(\frac{h}{2}\right)^2 h$
simplify the formula for V in terms of h , then take the derivative w/r to time.
you were given $\displaystyle \frac{dh}{dt} = 5$ ft/min ... calculate $\displaystyle \frac{dV}{dt}$ when h = 10 ft