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Math Help - Circular Cone Amount of Work problem

  1. #1
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    Circular Cone Amount of Work problem

    A tank in the shape of an inverted right circular cone has height meters and radius meters. It is filled with meters of hot chocolate.
    Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is

    This is the problem, how exactly do I solve it?
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  2. #2
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    In such an object, height and radius have constant proportions.

    radius / height = (17/2) / 7

    radius(h) = (17/14)h

    Check: radius(0) = 0 and radius(7) = (17/14)*7 = 17/2

    \int (HowMuchToPump)*(HowFarToPump)*Density

    HowMuchToPump = \pi r^{2} = \pi \left(radius(h)\right)^{2}

    HowFarToPump = 7 - h
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  3. #3
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    I don't think I calculated at all correctly. I got a huge sum.

    I'm not sure what the upper and lower bounds would be on that, and you seemed to vary radius and height continually. I'm not sure how you got your numbers
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  4. #4
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    Where does the 6 come into play? Would it be an h value at some point?
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  5. #5
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    1) That is a large collection of a dense fluid. It will take a lot of work.

    2) I deliberately left off the limits of integration. I was hoping you would tell me what those are. This may answer your '6' question.
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  6. #6
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    Use similar triangles:

    \frac{17}{7}=\frac{r}{y}

    r=\frac{17}{7}y

    The volume of a disk slice is {\pi}\left(\frac{17}{7}y\right)^{2}{\Delta}y={\pi}  \frac{289}{49}y^{2}dy

    \frac{419050\pi}{49}\int (7-y)y^{2}dy
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  7. #7
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    Ack! I have Diameter = 17 in my head. Listen to galactus.
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