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Math Help - Volume of the Sphere

  1. #1
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    Volume of the Sphere

    I don't know if this should be in Geometry or in Calculus since I've since quite a lot of derivations using calculus.

    I've always wondered how the Vol. of the Sphere = (4/3)(pi)(r^3) [I'm sorry I put 4(pi)(r^2)]
    So can I use steradians to prove it?

    So here's my way:
    The volume of a cone (I'm thinking that a steradian is a cone with a curved base) = 1/3(Are of the Base)(height)
    And there are 4 steradians in a sphere so
    4[(1/3)(2)(pi)(r^2)(h)]
    =(4/3)(pi)(r^2)(r) since the vertex of a steradian is at the center of the circle
    =(4/3)(pi)(r^3)



    Is this correct?
    Last edited by Volle; August 2nd 2012 at 03:50 AM.
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  2. #2
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    Re: Volume of the Sphere

    The volume of a sphere does NOT equal \displaystyle \begin{align*} 4\pi r^2 \end{align*}, it's \displaystyle \begin{align*} \frac{4}{3}\pi r^3 \end{align*}.

    Lesson EASY PROOF of volume of a sphere
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  3. #3
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    Re: Volume of the Sphere

    Okay so I can't edit my first post so I'm gonna reply here.
    I know that the SA of a sphere is 4(pi)(r^2) by steradians
    A steradian has a SA of (r^2) where r is the radius of the given sphere and there are 4(pi) number of steradians in a sphere.

    So I've got the volume of the sphere but I can't explain it.
    ([V{cone}][SA{sphere}])/Area{circle}

    where the cone has a sort of distorted base with its vertex at the centre of the circle. and with that in mind, its height is the radius of the sphere.

    So substituting the stuff,
    [(1/3)(pi)(r^2)(h)][4(pi)(R^2)]/(pi)(r^2)
    =[(1/3)(pi)(r^2)(R)][4(pi)(R^2)]/(pi)(r^2)

    where r is the radius of the circle, and R is the radius of the sphere.


    P.S. Please don't use calculus. I want to explain it to others as simple as possible. And I can't understand calculus.
    It makes sense, but I can't explain it.
    Someone help...
    Last edited by Volle; August 5th 2012 at 02:34 AM.
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  4. #4
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    Re: Volume of the Sphere

    what is wrong with the link provided by Prove it ? the proof shown there does not involve calculus.
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  5. #5
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    Re: Volume of the Sphere

    No, what I'm asking is, is my proof correct? And can you help on the explaining?
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