Waterisbeingpouredattherateof2⇡m3/min.intoaninvertedconicaltankthat is 12-meter deep with a radius of 6 meters at the top. If the water level is rising at the rate of 61 m/min and there is a leak at the bottom of the tank, how fast is the water leaking when the water is 6-meter deep?
For the conical tank with radius R=6 and height h=12
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 is h meter deep is
The volume in the tank increases at a rate
When the water depth is h=6 m and the rate of water volume increases is
With water entering the tank at 2 and water leaking out at unknown rate of
The water is increasing at a rate of
That means that
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