Math

A conical water tank with vertex down has a radius of 10 feet at the top and is 22 feet high. If water flows into the tank at a rate of 30 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 14 feet deep?

I have tried several times but keep getting .38197. Please help!

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asked by Sarah
  1. at depth y, the radius of the water surface is r = (10/22)x = 5/12 x

    So, at depth y, the volume of water is

    v = 1/3 π (5/12 y)^2 = 25/432 π y^2
    dv/dt = 25/216 π y dy/dt

    30 = 25/216 π (14) dy/dt
    30 = 5.08 dy/dt
    dy/dt = 5.89 ft/min

    As always, check my math.

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    posted by Steve

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