Question:

Challenging Related Rates- Inverted cone

by Guest6002 | 12 years, 7 month(s) ago

Water is leaking out of an inverted conical tank at a rate of 10500 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.

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amomipais82

Hi,
You need to get a volume formula in terms of a single variable.

\frac{r}{h} = \frac{2}{3}

r = \frac{2h}{3}

V = \frac{\pi}{3}\left(\frac{2h}{3}\right)^2 h

V = \frac{4\pi}{27} h^3

take the time derivative of the above volume function ... sub in your given values for \frac{dV}{dt} and h ... calculate the value of \frac{dh}{dt}.
Report (0) (1) | 12 years, 7 month(s) ago