As san leaks out of a hole

Question

Give your answer accurate to the nearest whole number.

As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at the rate of 6 in/min, find the rate (in cubic inches per minute) at which the sand is leaking out when the height is 12 in.

Answer 1

Answer 2

Let V = volume at time t

V = (1/3)πr²h

Since r = h, V = (1/3)πh³

dV / dt = πh²(dh/ dt)

When h = 12 and dh/dt = 6, dV / dt = π(12)²(6) = 864π in³/min