Elliptic Cone Volume

Find the volume of an elliptic cone from its semi-major axis, semi-minor axis, and height. Base area included.

Input

Enter the semi-major axis a, the semi-minor axis b, and the height h of the elliptical base to find the volume and base area of the elliptic cone.

Semi-major axis a

Semi-minor axis b

Height h

Volume V

75.398224

Base area πab

37.699112

Height h

Lengths use the same unit as the input. Area is in squared units and volume in cubed units.

An elliptic cone has an elliptical base and a single apex. Enter the semi-major axis a, the semi-minor axis b, and the height h to compute the volume.
The base area equals pi times a times b. When a equals b the base becomes a circle and the solid reduces to an ordinary circular cone.
The volume equals one third times the base area times the height, that is one third times pi times a times b times h. A cone holds one third of the prism with the same base and height.
The height h is the perpendicular distance from the apex to the base, not the slant length along the surface.
Use the same length unit for every input. Area is in squared units and volume is in cubed units of that length.

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