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A frustum is the portion of a solid – normally a cone or pyramid – which lies between two parallel planes cutting the solid. Degenerate cases are obtained for finite solids by cutting with a single plane only. Image File history File links Size of this preview: 500 × 500 pixelsFull resolution (500 × 500 pixel, file size: 48 KB, MIME type: image/png) La bildo estas kopiita de wikipedia:en. ...
A trapezoid (in North America) or trapezium (in Britain and elsewhere) is a quadrilateral, which is defined as a shape with four sides, which has a pair of parallel sides. ...
Look up polygon in Wiktionary, the free dictionary. ...
The symmetry group of an object (e. ...
The symmetry group of an object (e. ...
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ...
For other uses, see Solid (disambiguation). ...
This article is about the geometric object, for other uses see Cone. ...
This article is about the polyhedron pyramid (a 3-dimensional shape); for other versions including architectural Pyramids, see Pyramid (disambiguation). ...
Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ...
Pyramid Frustum
Pyramidal frusta are a subclass of the prismatoids. A prismatoid is a polyhedron where all vertices lie in two parallel planes. ...
The formula for the volume of the frustum is The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ...
 where h is the height from the top base to the bottom base, B1 is the area of the bottom base, and B2 is the area of the top base. (See also: Heronian mean.) A more intuitive formula is: the volume of the cone (or other figure) before you sliced the top off, minus the volume of the cone (or other figure) that you sliced off: The Heronian mean of two non-negative real numbers and is given by . ...
 The result comes from  and  .
Two frusta joined at their bases make a bifrustum. An n-agonal bifrustum is a polyhedron composed of three parallel planes of n-agons, with the middle plane largest and usually the top and bottom congruent. ...
Conical Frustum A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). For a right circular cone, let "h" be the height, "S" be the slant height, "R1" the base and "R2" the top radii.
Then
The surface area, not including the top and bottom circles, is
A = π(R1S1 − R2S2) The volume of the frustum is given by  But
so
This formula can be generalized to any pyramid by letting be the base areas of the top and bottom of the frustum. Then the volume can be written as
The area-weighted integral of over the frustum is
so the geometric centroid is located along the z-axis at a height
(Eshbach 1975, p. 453; Beyer 1987, p. 133; Harris and Stocker 1998, p. 105). The special case of the cone is given by taking , yielding .
Examples An example of a pyramidal frustum may be seen on the reverse of the Great Seal of the United States, as on the back of the U.S. one-dollar bill. The "unfinished pyramid" is surmounted by the "Eye of Providence". Obverse The Great Seal of the United States is used to authenticate certain documents issued by the United States government. ...
This article does not adequately cite its references or sources. ...
Certain ancient Native American mounds also form the frustum of a pyramid. A Hupa man. ...
The John Hancock Center in Chicago, Illinois is a frustum whose bases are rectangles. Several buildings bear this name, all built by John Hancock Insurance and named after John Hancock. ...
Nickname: Motto: Urbs In Horto (Latin: City in a Garden), I Will Location in the Chicago metro area and Illinois Coordinates: Country United States State Illinois County Cook & DuPage Incorporated March 4, 1837 Government - Mayor Richard M. Daley (D) Area - City 234. ...
Official language(s) English[1] Capital Springfield Largest city Chicago Largest metro area Chicago Area Ranked 25th - Total 57,918 sq mi (149,998 km²) - Width 210 miles (340 km) - Length 390 miles (629 km) - % water 4. ...
The Washington Monument is a narrow pyramidal frustum (with square bases) with a pyramid attached to the top base. The Washington Monument at dusk For other Washington Monuments, see Washington Monuments (world). ...
The focal field of a still or video camera forms a frustum. In 3D computer graphics, this is called the viewing frustum. Large format camera lens. ...
3D computer graphics are different from 2D computer graphics in that a three-dimensional representation of geometric data is stored in the computer for the purposes of performing calculations and rendering 2D images. ...
In 3D computer graphics, the viewing frustum or view frustum is the region of space in the modeled world that may appear on the screen; it is the field of view of the notional camera. ...
The spelling frustrum, listed as "erroneous" by the Oxford English Dictionary, is frequently encountered and might be considered a variant. The Oxford English Dictionary gives both frusta and frustums for the plural. The Oxford English Dictionary print set The Oxford English Dictionary (OED) is a dictionary published by the Oxford University Press (OUP), and is generally regarded as the most comprehensive and scholarly dictionary of the English language. ...
External links Look up frustum in Wiktionary, the free dictionary. | 
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