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## Homework Statement

Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.

## Homework Equations

V=1/3 pi(r)^2*h

relationships:

4/2r=6/h

therefore,

r=1/3h

Substituting h for r:

V=1/3 pi (1/3h)^2(h)

V=pi/27(h)^3

V'=dv/dt= pi/27 (3h)^2dh/dt

dv/dt=pi/27 (3*200)^2(20)

since the cone is leaking we have to find:

dv/dt-6500=pi/27(3*200)^2(20)