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Volume (also called capacity) is a quantification of how much space an object occupies. The SI unit for volume is the cubic metre (American spelling meter).The volume of a solid object is a numerical value given to describe the three-dimensional concept of how much space it occupies. One-dimensional objects (such as lines) and two-dimensional objects (such as squares) are assigned zero volume in three-dimensional space.
Volume in acoustics is used as a synonym for loudness. It is a common term for the amplitude or the level of sound. See also: DB(A), Sone, phon
Less commonly, in mathematics, volume can refer to the amount of space an n-dimensional object fills up, for some n > 3. Volumes are defined by means of integral calculus, by the decomposition of complex sets into small volume elements. Volume (Cx3) is the antiderivativeIn calculus, an antiderivative or primitive function of a given real valued function f is a function F whose derivative is equal to f i. F ' f''. The process of finding antiderivatives is antidifferentiation (or indefinite integration . For example: F ''x of areaThis article explains the meaning of area as a Physical quantity. Article area (geometry) is more mathematical. Area is a quantity expressing the size of a region of space. Surface area refers to the summation of the areas of the exposed sides of an objec (Cx2). More simply, for a perfect closed curve, which is the sphere in three dimensions, the volume is the simple integral of the surface area. Thus, the surface area of a sphere is 4πr2, and the volume is (4/3)πr3.
1 Volume formulae
Common equationAlgebra This article is about equations in mathematics. For equations in chemistry, see chemical equation. In mathematics, one often (not quite always) distinguishes between an identity which is an assertion that two expressions are equal regardless of ths for volume:
- A cubeThree dimensions A cube (or hexahedron is a Platonic solid composed of six square faces, with three meeting at each vertex. The cube is a special kind of square prism, of rectangular parallelepiped and of triangular trapezohedron, and is dual to the octah:
(where s is the length of a side)
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- A rectangular prismpolyhedra In geometry, a prism is a polyhedron made of two parallel copies of some polygonal base joined by faces that are rectangles or parallelograms. In the case these joining faces are rectangular, the object is said to be a right prism . The rectangu:
(length, width, height)
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- A cylinderThe word cylinder has several meanings. For the geometric object, see Cylinder (geometry . For the engine component, see Cylinder (engine . In firearms the cylinder is the rotating device that contains the firing chambers of a revolver. The phonograph cyl:
(r = radius of circular face, h = distance between faces)
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- A sphereFor other uses, see sphere (disambiguation). A sphere is, roughly speaking, a ball-shaped object. In non-mathematical usage a sphere is often considered to be solid (which mathematicians call ball . But in mathematics, a sphere is the boundary of a ball,:
(r = radius of sphere)
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- An ellipsoid:
(a, b, c = semi-axes of ellipsoid)
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- A pyramid:
(A = area of base, h = height from base to apex)
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- A cone (circular-based pyramid):
(r = radius of circle at base, h = distance from base to tip)
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- Any prism that has a constant cross sectional area along the height**:
(A = area of the base, h = height)
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- Any figure ( calculus required):
(where h is any dimension of the figure, and A(h) is the area of the cross-sections perpendicular to h described as a function of the position along h; this will work for any figure (no matter if the prism is slanted or the cross-sections change shape).
