Question

An inverted conical tank is being filled with water, but it is discovered that it is also leaking water at the same time. The tank is 6 meters high and its diameter at the top is 4 meters. The water is being added to the tank at a constant rate. Some of this water is found to be leaking at a rate of 8,500 cm3/min. Suppose that the water level in the tank is found to be rising at a rate of 20 cm/min when the height of the water is 2 meters. Find the rate at which water is being added to the tank.

Answer 1

when the water has height y, its surface has diameter 4/6 y.

So,

v = 1/3 pi y^2 (2y/3) = 2/9 pi r^3

dv/dt = 2/3 pi r^2 dr/dt

Now just plug in your numbers.

Answer 2

167.5516