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In geometry, a frustum (Latin for 'morsel'); [a] (pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal .
Concrete cone is one of the failure modes of anchors in concrete, loaded by a tensile force. The failure is governed by crack growth in concrete, which forms a typical cone shape having the anchor's axis as revolution axis .
The test is carried out using a metal mould in the shape of a conical frustum known as a slump cone or Abrams cone, that is open at both ends and has attached handles.The tool typically has an internal diameter of 100 millimetres (3.9 in) at the top and of 200 millimetres (7.9 in) at the bottom with a height of 305 millimetres (12.0 in).The cone is placed on a hard non-absorbent surface.
For a regular n-gonal bifrustum with the equatorial polygon sides a, bases sides b and semi-height (half the distance between the planes of bases) h, the lateral surface area A l, total area A and volume V are: [2] and [3] = (+) () + = + = + + Note that the volume V is twice the volume of a frusta.
The lateral surface area of a right circular cone is = where is the radius of the circle at the bottom of the cone and is the slant height of the cone. [4] The surface area of the bottom circle of a cone is the same as for any circle, . Thus, the total surface area of a right circular cone can be expressed as each of the following: Radius and ...
A square frustum, with volume equal to the height times the Heronian mean of the square areas. The Heronian mean may be used in finding the volume of a frustum of a pyramid or cone. The volume is equal to the product of the height of the frustum and the Heronian mean of the areas of the opposing parallel faces. [2]
A spherical segment Pair of parallel planes intersecting a sphere forming a spherical segment (i.e., a spherical frustum) Terminology for spherical segments.. In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes.
For a cube the lateral surface area would be the area of the four sides. If the edge of the cube has length a, the area of one square face A face = a ⋅ a = a 2. Thus the lateral surface of a cube will be the area of four faces: 4a 2. More generally, the lateral surface area of a prism is the sum of the areas of the sides of the prism. [1]