calculus

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Water is poured into a conical tank 6m across the top and 8m deep at the rate of 10m/min. How fast is the water level rising when the water in the tank is 5m deep?

  • calculus -

    radius of water level --- r
    height of water level --- h

    by ratio:
    r/h = 6/8
    8r= 6h
    r = 3h/5

    V = (1/3)πr^2 h
    = (1/3)π(9h^2/25)(h)
    =3/25)πh^3
    dV/dt = (9/25)π h^2 dh/dt
    given: when h = 5 , dV/dt = 10
    10 = (9/25)π (25) dh/dt
    dh/dt = 10/(9π)

    check my arithmetic

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