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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 - https://domyhomework.club/geometry-homework/ . 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

AG:AD=h1^2:h2^2

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

AO=AG+AD+AM

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

V=1/3h(AG+√AGAD+AD)

Ellipsoid

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:

V=4/3π⋅x⋅y⋅z

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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