Volume of an Elliptical FrustumDate: 12/01/1999 at 07:46:49 From: Alan Macleod Subject: An elliptical frustum Dear Doc, I'm still confused! Please help. From Deriving the Volume of a Frustum http://mathforum.org/dr.math/problems/taylor5.6.98.html the volume of a frustum is V = (1/3)*pi*(R^2*H - r^2*(H-h)) and H = Rh/(R-r) From other articles: The volume of a cone is V = (1/3)*pi*R^2*h and the volume of an elliptical cone is V = (1/3)*pi*a*b*h Can I therefore assume that the volume of a elliptical frustum is: V = (1/3)*pi*[(a*b)*H - (c*d)*(H-h)] and (sqrt(a*b))*h H = --------------------- sqrt(a*b) - sqrt(c*d) where a = semi-major axis of base b = semi-minor axis of base c = semi-major axis of top d = semi-minor axis of top If not, then can you give me the correct formulas? Date: 12/01/1999 at 10:02:08 From: Doctor Rob Subject: Re: An elliptical frustum Thanks for writing to Ask Dr. Math, Alan. Yes, the volume of an elliptical frustum is V = (1/3)*pi*[(a*b)*H - (c*d)*(H-h)] The last part is also correct, but you can avoid the square roots if you realize that a/c = b/d = H/(H-h). Then you can use instead H = a*h/(a-c) = b*h/(b-d) - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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