Need help deriving an equation

chris777

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]

Jameson

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?

dextercioby

[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.

chris777

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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chris777	Need help deriving an equation 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]

Jameson	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?

dextercioby Blog Entries: 9 Recognitions: Homework Help Science Advisor	[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.

chris777	Need help deriving an equation 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.