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suppose you are drinking root beer from a conical cup. the cup has a diameter of 8 cm and a depth of 10 cm. as you suck the straw, root beer leaves the cup at the rate of 7 cm^3/second. at what rate is the level of the liquid in the cup changng when the liquid is 6 cm deep?

  • math -

    rate of change of volume = surface area * rate of change of depth
    (look at thin slice of area pi r^2 and depth delta h)

    what is r?
    4/10 = r/6 similar triangles
    r = 12/5
    surface area = pi(144/25)
    so
    -7 cm^3/s = pi(144/25) cm^2 * dh/dt
    so
    dh/dt = -(25*7)/(144 pi) cm/s

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