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Math Help - Which formula you reckon?!

  1. #1
    Junior Member User Name's Avatar
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    Post Which formula you reckon?!

    Hi guys which formula suit this Question?
    thanks
    Last edited by User Name; May 24th 2008 at 11:49 PM.
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  2. #2
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    Hello, User Name!


    I'll number the formulas like this: . \begin{array}{cc} (1) & (2) \\ (3) & (4) \\ (5) \end{array}


    Formula (1): . V \;=\;\pi\left(\frac{a+b}{2}\right)^2
    . . \pi r^2 is the area of the circle. . \frac{a+b}{2} is the average of the two radii.

    Therefore, (1) gives the area of the "average circle".
    . . I seriously doubt that this happens to be the volume of the doughnut.



    Formula (3): . V \:=\:\frac{\pi}{3}(a^3 + b^3)
    . . \frac{4}{3}\pi r^3 is the volume of a sphere.

    . . We have: . \frac{1}{4}\left[\frac{4}{3}\pi a^3 + \frac{4}{3}\pi b^3\right]

    This is the volume of a sphere of radius a
    . . plus the volume of a sphere of radius b
    . . divided by 4.

    This is too large to be the volume of the doughnut.



    Formula (4): . V \;=\;\pi^3(b^2-a^2)

    We have: . \pi^2\left(\pi b^2 - \pi a^2\right)

    . . \pi b^2 is the area of the outer circle.
    . . \pi a^2 is the area of the inner circle.
    . . \pi b^2 - \pi a^2 is the area of the "ring".

    I don't think multiplying by \pi^2 will give us the volume of the dougnut.



    Formula (5): . V \;=\;\frac{\pi^2}{3}(a + b)^3
    We have: . \frac{\pi}{4}\left[\frac{4}{3}\pi (a+b)^3\right]

    This the volume of a sphere of radius a+b ... (quite large!)
    . . multipled by \frac{\pi}{4}

    This is far too large to be the volume of the doughtnut.



    By elimination, . (2)\;\;V \:=\:\frac{\pi^2}{4}(a+b)(b-a)^2 .is the volume of the doughnut.

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  3. #3
    Junior Member User Name's Avatar
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    Thanks Soroban Once again
    I think Your right as usual
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