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math

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Water is being pumped into an inverted right circular conical tank at the rate 30 ft^3/min. the tank, which stands vertex down and base up, has a height of 12 ft and a base diameter of 16 ft. how fast is the water level rising when the water is 9 ft deep?

  • math - ,

    at depth h, h = 3/2 r

    v = 1/3 pi r^2 h
    v = 1/3 pi r^2 (3r/2)
    v = pi/2 r^3

    dv/dt = 3pi/2 r^2 dr/dt

    30 = 3pi/2 * 36 dr/dt
    dr/dt = 5/(9pi)

  • math - ,

    thanks steve

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