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Homework Help: Need help deriving an equation

  1. Mar 12, 2005 #1
    I can't figure out how to derive this. This is the formula for the volume of a cone. R is a constant and the side of the cone. Can be any real number.

    If anyone could take a crack at deriving this id be very greatful!

    [tex]V = \pi/3 * (R(1 - x/2\pi))^2 * \sqrt{(R^2 - (R(1 - x/2\pi))^2}[/tex]
     
  2. jcsd
  3. Mar 12, 2005 #2
    Is that your formula or the one you need to derive? And what exactly are you tring to derive? The formula for the volume of a cone?
     
  4. Mar 12, 2005 #3

    dextercioby

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    [tex]V=\frac{\pi r^{2}h}{3} [/tex]

    .If the (semi)cone is rectangular (the axis joining the top and the center of the base (assumed a circle)),then u can use Pythagora's theorem

    [tex] R^{2}=r^{2}+h^{2} [/tex] and then can express the volume in terms of "R" and either the height "h",or the radius of the circle (the base) "r".

    Daniel.
     
  5. Mar 12, 2005 #4
    r = R(1-x/2pi)
    h = sqrt( R^2 - ( R (1-x/2pi)))

    these are put into the formula for the volume of the cone. Now I need to derive that equation to know which x will give the max volume of the cone.
     
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