SOLUTION: Water is being poured at the rate of 2pi cubic meter per minute into an inverted conical tank that is 12 m deep with the radius of 6 m at the top. If the water level is rising at

Question 1117080: Water is being poured at the rate of 2pi cubic meter per minute into an inverted conical tank that is 12 m deep with the radius of 6 m at the top. If the water level is rising at the rate of 1/6 m/min and there is a leak at the bottom of the tank, how fast is the water leaking when the water is 6-m deep?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For the conical tank, with radius and height ,
<--> .
Whatever the water level, the water in the tank is a cone
similar in shape to the tank itself, with .

The volume of water in the tank when the water id m deep is
,
with in m and in .
The volume in the tank increases at a rate, in of
.
When the water depth is , ,
and the rate of water volume increase, in , is
.

With water entering the tank at ,
and water leaking out at an unknown rate of ,
the water volume is increasing at a rate of .
That means that
-->

When the water depth is 6m, water is leaking at cubic meters per minute.
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