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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 .
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 ...
Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line.
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]
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.
Parasitic cone (in foreground) with larger main cone in background, at Piton de la Fournaise volcano on the island of Réunion. A parasitic cone (also adventive cone, satellite cone, satellitic cone or lateral cone) is the cone-shaped accumulation of volcanic material not part of the central vent of a volcano.