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 squaress) are assigned zero volume in three-dimensional space.
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 antiderivative of area (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 4/3πr3.
A cone: π r2 h / 3 (r = radius of circle at base, h = distance from base to tip)
any prism that has a constant cross sectional area along the height**: A h (A = area of the base, h = height)
any figure (calculus required): ∫ A dh (where h is any dimension of the figure, and A 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).
A commonly used SI unit for volume is the litre (American spelling liter), and one thousand litres is the volume of a cubic metre, which was formerly termed a stere. A cubic centimeter is the same volume as a millilitre.
