Conic solid

A conic solid is the locus of all line segments between a simply connected region of a plane (the base) and a point (the apex) outside the plane. It is the generalization of a pyramid to non-polygonal bases. Cones are also conic solids.

Related Topics:
Locus - Simply connected - Pyramid - Cones

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The volume of any conic solid is one third the area of the base times the height (the perpendicular distance from the base to the apex). This can be proven with calculus by approximating the conic solid with pyramids, and letting the number of pyramids increase without bound, so the sum of their volumes approaches the total volume of the conic solid.

Related Topics:
Volume - Calculus

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Alternatively it can be proven as follows. A cross section parallel to the base is similar to the base with a linear size proportional to the distance to the apex. Therefore its area is proportional to the square of the distance to the apex. Integrating the area gives the volume formula.

Related Topics:
Cross section - Similar

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The center of mass of a conic solid is at a height of 1/4 of the total height, from the base.

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The boundary of a conic solid is (part of) a conic surface. In general there is no formula for the surface area of a conic solid; calculus is necessary.

Related Topics:
Boundary - Conic surface - Surface area

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