Volume of ellipsoidDate: 05/22/97 at 22:51:42 From: Anonymous Subject: Calculation of the volume of ellipse Dear Dr. Math, I have forgotten how to calculate the volume of an ellipse. I guess the volume of ellipse with radius of a and b should be (2/3*pi*a^2*b) where a is shorter radius and be is longer radius. Would you teach me the soultion and tell me where I can find information in internet? With my best regards, Wonil Chung Date: 05/23/97 at 06:17:27 From: Doctor Mitteldorf Subject: Re: Calculation of the volume of ellipse Dear Wonil Chung, Language is making it hard for us. An ellipse is a plane figure, in 2 dimensions. Volume is 3-dimensional. I think you want to ask about the volume of an ellipsoid. An ellipsoid is a 3-D figure, like a sphere, but it can have 3 different radii in 3 directions. Maybe you are thinking of an "oblate ellipsoid of revolution" where twoof these are the same. This is a watermelon shape, or a cigar shape. The formula for the volume of a sphere is 4/3 pi r^3. You can scale each of the 3 dimensions separately, and generalize this to the volume of an ellipsoid with semi-axes a, b, and c. The answer is just 4/3 pi a*b*c. If two of them are the same, the volume is 4/3 pi a^2*b Any math handbook has these formulas. Have you studied calculus? If you set up the integrals for a sphere and for an ellipsoid, you can easily show the relation between the two volume formulas. You might also just think about it and see if you can convince yourself that it is true that the formula for the volume of an ellipsoid is just the same as the formula for a sphere, but with each axis "stretched" appropriately. -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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