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单词 Volume
释义

volume


Note that a solid is a three-dimensional figure.

The volume of a solid is the amount of space contained within the solid. Volume is typically measured in (also called ); i.e. (http://planetmath.org/Ie), if the volume of a solid is 5 in3, this means that, if five 1 inch by 1 inch by 1 inch cubes are cut appropriately, they can be arranged so that they exactly fill the solid without any overlapping. In formulasMathworldPlanetmathPlanetmath, volume is almost always denoted using the letter V.

All examples provided within this entry are in Euclidean geometryMathworldPlanetmath.

For certain solids, volume is quite commonly found by multiplying the lengths of three (not necessarily distinct) line segmentsMathworldPlanetmath which are related to the solid. Some examples are:

  • cylinders

  • prisms

  • cones

  • pyramidsMathworldPlanetmath

  • spheres

With the exception of spheres, each of these solids has at least one face that serves as its base. Cylinders and prisms have two bases; for these solids, the height is defined to be the line segment that is perpendicularPlanetmathPlanetmathPlanetmath to both bases and whose endpoints lie on the bases. If a cylinder or prism has a base of area B and a height of length h, then its volume is:

V=Bh

Cones and pyramids have one base; for these solids, the height is defined to be the line segment that is perpendicular to the base, has one endpoint on the base, and has the apex of the figure as its other endpoint. If a cone or pyramid has a base of area B and a height of length h, then its volume is:

V=13Bh

The volume of a sphere is given by V=43πr3.

Remarks

  • Finding the volume of more complicated geometric figures requires knowledge of calculus. In fact, the formulas given above can all be derived using calculus.

  • The concept of volume is a special case of a more general concept called measureMathworldPlanetmath, or more appropriately, product measureMathworldPlanetmath.

Titlevolume
Canonical nameVolume
Date of creation2013-03-22 17:12:58
Last modified on2013-03-22 17:12:58
OwnerWkbj79 (1863)
Last modified byWkbj79 (1863)
Numerical id11
AuthorWkbj79 (1863)
Entry typeDefinition
Classificationmsc 51-00
Classificationmsc 51M25
Related topicArea2
Related topicPrismatoidMathworldPlanetmath
Related topicBasicLength
Related topicExampleOfRiemannTripleIntegral
Definessolid
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更新时间:2025/5/4 21:58:08