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nekita · Jan 19, 2011, 05:38 PM

A water tank has the shape of an inverted circular cone with a base radius 2 m and a height 4 m. If the water is being pumped into the tank at rate 2m^3/min , find the rate at which the water level is rising 3m.

help please =/?

Unknown008 · Jan 19, 2011, 11:25 PM

The volume of the cone is given by:

$V = \frac13 \pi r^2 h$

Also, from the height and radius, you know that:

$\frac{h}{r} = \frac42$

What you know are:

$\frac{dV}{dt} = 2$

You are requested to give:

$\frac{dh}{dt}$

Use the chain rule:

$\frac{dV}{dt} = \frac{dV}{dh} \times \frac{dh}{dt}$

Hence, find V in terms of h, find the derivative of the volume of cone formula, replace in the equation with h = 3 m.

What do you get? :)