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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