Math related rates

Water is poured into a conical paper cup at the rate of 3/2 in3/sec
(similar to Example 4 in Section 3.7). If the cup is 6 inches tall and the top
has a radius of 4 inches, how fast is the water level rising when the
water is 2 inches deep?

I got (81)/(128*3.14) but it keeps saying my answer is wrong. Please help

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  1. if the water depth is h, the radius of the surface is 2/3 h. So, the volume of water is

    v = 1/3 πr^2 h
    = 1/3 π (2/3 h)^2 h
    = 4/27 πh^3

    dv/dt = 4/9 πh^2 dh/dt
    plugging in the numbers,

    3/2 = 4/9 π*2^2 dh/dt
    dh/dt = 27/(32π)

    Too bad you didn't bother to show your work...

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  2. thank you

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