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Homework Help: Torricelli's Law (Seperable DE Application)

  1. Jan 28, 2014 #1
    1. The problem statement, all variables and given/known data
    A spherical tank of radius 4(ft) is full of gasoline when a circular bottom hole with radius 1 in. is opened. How long will be required for all the gasoline to drain from the tank?

    2. Relevant equations

    dVolume/dTime = -a(2gy)^(1/2)

    3. The attempt at a solution
    Right now i'm trying to find an equation to express the cross sectional area of the sphere in terms of y. The answer solution manual I am looking out says that A(y) = ∏(4^2 - (4-y)^2). However, I don't see how this can be correct as that would mean the cross section area when y=4 is equal to ∏*16, which is obviously false, because the top of a sphere should have cross sectional area of 0. It works when you enter 0 in for y however. Help?
  2. jcsd
  3. Jan 28, 2014 #2


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    Homework Helper

    The sphere has radius 4, so if its bottom is at [itex]y = 0[/itex] then its center is at [itex]y = 4[/itex] and its top is at [itex]y = 8[/itex].
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