﻿ Frustum

# Frustum

A truncated pyramid is a term from the geometry that describes a specific type of polyhedra ( Vielflächnern ). A truncated pyramid is created by the fact that one of a pyramid ( output pyramid ) cut parallel to the base, a smaller, similar pyramid ( Pyramid supplement ).

The two parallel faces of a truncated pyramid are similar to each other. The larger of these two surfaces is known as the base, smaller than the top surface. The distance between the base and top surface is called the height of the truncated pyramid.

The volume of a truncated pyramid, can be calculated using the following formula:

Here are the base for A1, A2 for the top surface and h is the height of the truncated pyramid.

For the outer surface, there is no simple formula. It can be any size at very oblique pyramids and truncated pyramids.

## Evidence

### Volume

Be defined as the height of h1 and h2 as output pyramid level of the pyramid supplement for the calculation of the volume of a truncated pyramid. From the central extension follows that

K is the stretch factor at a central extension.

The point S in the figure serves as the center of the expanded construction of the starting and completion pyramid.

The volume of the truncated pyramid is derived from the difference between the volume of the output pyramid and the volume of the supplementary pyramid.

Off and

Applies:

Substitution: = →

Thus one can rewrite the volume:

Using the formula:

And substitution

Is the volume

Or more simply

The factor is the height h

=.

=

- = H

It follows

## Degeneracies

• Pursuit base and top surface to a circle, you get a truncated cone, is valid for the same volume formula.
• Aims A2 to A1, one obtains a prism whose volume formula, A2 = A simplified accordingly by A1 =.
• Aims A2 to 0, we obtain a pyramid.

## Swell

Rolf Baumann: Geometry for the 9-10. Class. Centric stretching, the Pythagorean theorem, circular and body calculations. 4th edition. Mentor -Verlag, Munich 2003, ISBN 3-580-63635-9.

• Polyhedron
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