The 'volume' of an object is, classically, a (positive) value given to describe the 3-dimensional concept of how much space said object 'uses up'. This means that neither a 1-dimensional object (a line), nor a 2-dimensional object, has a defined 3-dimensional volume (it has volume of zero). It can also be used to refer to the amount of space an n-dimensional object uses up. although this usage is uncommon.
Common equations for volume:
- A cube: s3 (where s is the length of a side)
- A rectangular prism: l * w * h (length, width, height)
- A cylindar: &pi * r2 * h (r = radius of circular face, h = distance between faces)
- A sphere: 4 * &pi * r3 / 3 (r = radius of sphere)
- 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): ∫Adh (where h is any dimension of the figure, and A is the area of the cross sections pependicular to h described as a function of the position along h)
-> **note: this will work for any figure (no matter if the prism is slanted or the cross sections change shape as long as the area remains the same!)
A commonly used SI unit for volume is the liter, and one thousand liters is the volume of a cubic meter.