The volume of a solid 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 (they each have a 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 cylinder: π r2 h (r = radius of circular face, h = distance between faces)
- A sphere: 4 π 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): ∫ A dh (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 of the cross sections parallel to the base are all equal).
To help compare different volumes, see these pages: