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Related Rates and a Conical Tank

  1. Nov 26, 2006 #1
    A water tank is in the shape of an inverted cone with depth 10 meters and top radius 8 meters. Water is flowing into the tank at 0.1 cubic meters/min but leaking out at a rate of 0.001h2 cubic meters/min, where h is the depth of the water in the tank in meters. Can the tank ever overflow?

    Can anyone help with this? The flowing in and leaking out is a bit confusing.
  2. jcsd
  3. Nov 26, 2006 #2
    [tex] V = \frac{1}{3}\pi r^{2} h [/tex]

    You know that [tex] \frac{r}{h} = \frac{4}{5} [/tex], so [tex] r = \frac{4h}{5} [/tex]

    So the new expression is: [tex] V = \frac{1}{3}\pi (\frac{4h}{5})^{2}h = \frac{16\pi}{75}h^{3} [/tex]

    You also know that [tex] \frac{dV}{dt} = 0.1 - 0.001 [/tex]
    Last edited: Nov 26, 2006
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