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### Volume of ellipsoid

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Date: 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)

Would you teach me the soultion and tell me where I can find
information in internet?

With my best regards,
Wonil Chung
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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
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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Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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