Topic: Ellipsoid Volume
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What is the formula for the volume of an ellipsoid?
Answer 'If a, b, and c are the semi-axes, the volume is (4/3)πabc. When a=b=c the ellipsoid is a sphere and this formula becomes (4/3)πa3' (James and James, eds, Mathematics Dictionary D. Van Nostrand, 1960) Read More »
Source: http://wiki.answers.com/Q/What_is_the_formula_for_the_volume_of_a...
What is the volume of an ellipsoid?
The volume of an ellipsoid is given by the formula \frac{4}{3}\pi abc.\,\! Read More »
Source: http://www.chacha.com/question/what-is-the-volume-of-an-ellipsoid
How do I derive the volume equation for an ellipsoid?
First calculate the area of ellipse: x^2/a^2 + y^2/b^2 = 1. It is the area under the curve y from 0 to a multiplied by 4. Area under the curve is: integral(from x=0 to x=a)[ b*sqrt(1-x^2/a^2) ] = |substitute x = a*sin(t), for x=0 t=0, for x... Read More »
Source: http://answers.yahoo.com/question/index?qid=20091213113816AAYyw7Z
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Ellipsoid Volume
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The smallest volume for an ellipsoid containing a regular parallelepiped happens when the ellipsoid circumscribes the parallelepiped (ie. all 8 vertices lie on the parallelepiped). The axes of the ellipsoid will correspond to the lines goin...
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Source: http://answers.yahoo.com/question/index?qid=20070617202050AAYBRyl
the answer is [4/3] π abc for x²/a² +y²/b² + z²/c² = 1, if you wish to prove that formula then you do integration in spherical coordinates...go to wikipedia.org and type in "ellipsoid"
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Source: http://answers.yahoo.com/question/index?qid=20090521173659AAD62U7
The volume of sphere is (4/3)πrrr. The volume of ellipsoid, which is oblate sphere is (4/3)πabc. Maximum volume of cube inside sphere is (2r/√3)(2r/√3)(2r/√3). Maximum volume of box, which is oblate cube, inside sphere is (2a/√3)(2b/√3)(2c/...
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Source: http://answers.yahoo.com/question/index?qid=20070509153940AAhrCNw
