Question

Salt is falling on a Conical pile of 6 cubic meters per minute. The diameter of the cone is twice the height, what is the rate the height is changing when the pile is 9 meters tall.

Answer 1

0.0236 m per minute,

Explanation:

Volume of the cone V = 1/3 π r^2 h.

Diameter = 2r = 2h so r = h

and V = 1/3 π h^3

So the rate of change of volume with height =

dV / dh = π h^2.

We are given that dV/dt = 6.

So the rate of change of height: dh/dt = dV/dt * dh/dV

= 6 * 1/ π h^2

When h = 9

dh/dt = 6 / 81π m per minute

= 0.0236 m per minute,