Calculus

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A cone-shaped coffee filter is draining at a rate of 20 in^3 /min. The filter has a diameter of 8 inches. the radius of the filter is 2/3 the height. how fast is the coffee level falling when the coffee is 3 inches deep?

  • Calculus -

    v = 1/3 pi r^2 h
    r = 2h/3, so
    v = pi/3 (4h^2/9) h
    = 4pi/27 h^3

    dv/dt = 4pi/9 h^2 dh/dt
    -20 = 4pi/9 * 9 dh/dt
    -5/pi = dh/dt

  • Calculus -

    idk what that is hehe

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