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Math Help - volume of cone

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    volume of cone

    Use integration to write aformula that gives the volume of cone , the radius of whose base is r and whose height is h
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    Quote Originally Posted by BAHADEEN View Post
    Use integration to write aformula that gives the volume of cone , the radius of whose base is r and whose height is h
    File:VOLUME OF CONE BY INTEGRATION.pdf - Wikimedia Commons
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    Quote Originally Posted by BAHADEEN View Post
    Use integration to write aformula that gives the volume of cone , the radius of whose base is r and whose height is h
    Alternatively,

    R=radius,\;H=height,\;r=varying\;cross-sectional\;radius,

    h=height\;of\;internal\;cone\;of\;radius\;r


    \displaystyle\frac{R}{H}=\frac{r}{h}=constant\Righ  tarrow\ R=Hk,\;\;r=hk

    The constant is tan\theta but this form is unnecessary.

    \displaystyle\int_{0}^H{{\pi}r^2}dh={\pi}k^2\int_{  0}^H{h^2}dh

    \displaystyle\ ={\pi}k^2\frac{H^3}{3}=\frac{{\pi}R^2}{H^2}\;\frac  {H^3}{3}=\frac{{\pi}R^2H}{3}
    Last edited by Archie Meade; January 4th 2011 at 01:01 PM. Reason: integrated over h, along x-axis
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