Need help deriving an equation

  • Thread starter chris777
  • Start date
  • #1
9
0
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]
 

Answers and Replies

  • #2
793
4
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?
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
13,162
725
[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.
 
  • #4
9
0
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.
 

Related Threads on Need help deriving an equation

Replies
3
Views
6K
Replies
1
Views
824
  • Last Post
Replies
2
Views
1K
Replies
1
Views
757
Replies
4
Views
914
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
Top