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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.

Respuesta :

Answer:

0.0236 m per minute,

Step-by-step 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,

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