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    calculus help

    A right circular cylinder has a diameter of 12 in. and a height of 12 in. If water is flowing in at the rate of 4pi in^3 per minute, find the rate of change of the height when the height is 4 in
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    A right circular cylinder has a diameter of 12 in. and a height of 12 in. If water is flowing in at the rate of 4pi in^3 per minute, find the rate of change of the height when the height is 4 in
    Rate of change of h.
    So we need to find dh/dt.

    At any time t,
    Volume, V = (pi r^2)h
    Since r does not change with time, then r is a constant, so,
    V = pi (12/2)^2 h
    V = (36pi)h
    Differentiate both sides with respect to time t,
    dV/dt = (36pi)(dh/dt) -------------(i)

    Since dV/dt is given as 4pi cu.in. per min,
    4pi = (36pi)(dh/dt)
    dh/dt = 4pi / 36pi
    dh/dt = 1/9 in./min. -----------answer.

    In (i), we see that the variables are (dV/dt) and (dh/dt) only. That means h is not factor, so, at any h, at h=1, h=4, h=9, the dh/dt is the same until the cylinder is filled up.
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