How to Calculate Elliptical Volume

An ellipse is a two-dimensional geometric figure formed by the intersection of a cone and a plane. An ellipsoid is the three-dimensional equivalent of an ellipse, and may be commonly described as a flattened sphere. The volume of an ellipsoid may be calculated from the length of its three axes.

Things You'll Need

• Calculator

Instructions

1. Express the ellipsoid in an xyz-Cartesian coordinate system. The standard equation of an ellipsoid is given by x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. This form has the center of the ellipsoid at the center of the coordinate system and has the axes of the ellipsoid aligned with the axes of the coordinate system.

2. Determine the radii of the ellipsoid. This is given by the variables a, b and c in the equation from Step 1. The variable a is the radius along the x axis, b is the radius along the y axis and c is the radius along the z axis.

3. Calculate the volume of the ellipsoid. This is given by the equation V = 4/3 pi abc where a, b, and c are the three radii of the ellipsoid.

4. Find the volume of a specific ellipsoid. If you can represent the ellipsoid with the equation x^2/2^2 + y^2/3^2 + z^2/5^2 = 1, the volume of the ellipsoid is given by the equation V = 4/3 pi abc = 4/3 pi (2)(3)(5) = 4/3 pi (25) = 100/3 pi.

5. Note that in the case of a sphere, a=b=c=r, where r is the radius of the sphere. The equation V = 4/3 pi abc reduces to V = 4/3 pi r^3, which is the volume of a sphere.

References

• SolveMyMath.com