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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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