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Truncated pyramid

If a pyramid is intersected by a plane parallel to the base of the pyramid, a truncated pyramid and the corresponding supplementary pyramid are created - . The base and top surfaces of the truncated pyramid, which are parallel to each other, have the distance h with

h =h1 - h2

(h1 height of the total pyramid, h2 height of the supplementary pyramid).

The base and top surfaces are similar to each other. The following applies to their surface areas


The mantle of a truncated pyramid is the sum of the trapezoidal side faces. For the surface area of a truncated pyramid applies:


The volume of a truncated pyramid is the difference between the volume of the entire pyramid and the supplementary pyramid. It holds:



An ellipsoid is a body of revolution that is created, for example, by the rotation of an ellipse around one of its main axes. While all three spatial expansions are the same for a sphere - geometry problem solver , they are different for an ellipsoid. An ellipsoid has three mutually perpendicular planes of symmetry and three principal axes x, y and z. All intersecting surfaces that run parallel to one of the three planes of symmetry are ellipses.

The volume of an ellipsoid is given by:


Our Earth is also not a sphere, but an ellipsoid - homework for you , because the equatorial radius (6 378 km) and the polar radius (6 356 km) are not the same.

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