Sand falls onto a conical pile at the rate of 10 cubic feet per minute. The radius of the pile is always equal to one half it altitude. How

Question

Sand falls onto a conical pile at the rate of 10 cubic feet per minute. The radius of the pile is always equal to one half it altitude. How fast is the altitude of the pile increasing when the pile is 5 feet high?​

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Thu Thủy 4 years 2021-09-05T00:33:39+00:00 1 Answers 10 views 0

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  1. RuslanHeatt
    0
    2021-09-05T00:34:56+00:00
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    Answer:

    Either one of these.

    Step-by-step explanation:

    volumepile=1/3 (PI r^2)h

    but r=h/2, so

    volume=1/12 PI h^3

    dv/dt=10 ft^3/min

    but dv/dt=1/12 PI 3h^2 dh/dt

    solve for dh/dt

    This assumes you mean by “altitude” the height. If you mean altitude as slant height, you have to adjust the fromula

    _______________________________________________

    given: r = h/2

    V = (1/3)π r^2 h

    = (1/3)π (h/2)^2 (h)

    = (1/12) π h^3

    dV/dt = (1/4)π h^2 dh/dt

    for the given data …

    10 = (1/4)π(25)dh/dt

    dh/dt = 10(4)/((25π) = 1.6/π feet/min

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