Volume

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.