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2 August, 04:53

Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 16cm and a height of 8cm, at the rate of 4 cm3/min. At what rate is the depth of the water changing at the instant when the water in the tank is 6 cm deep? Show all work and include units in your answer. Give an exact answer showing all work and include units in your answer.

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  1. 2 August, 05:13
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    Let h=height of water

    Let r=radius of water surface

    r/h=16/8 = 2, so r=2h.

    The volume of water is:

    v = (1/3) * π*r²*h

    = (1/3) * π * (2h) ²*h

    =4/3πh³

    dv/dh=4πh^2

    By chain rule:

    dv/dt=dv/dh*dh/dt

    but

    dv/dt=4

    thus:

    4 = (4πh) * dh/dt

    dh/dt=4 / (4πh²)

    when h=6cm we have:

    dh/dt=4 / (4π6²)

    =0.00884 cm³/min
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