Volume

The volume, of an object, is a quantification of how much space it "takes
up". The volume, of an object, is equal to its mass divided by its average
density. Volume (Cx3) is the antiderivative of area (Cx2). In terms of
volume measurements, volume may also be termed "capacity".

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 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 liter, and one thousand liters is
the volume of a cubic meter, which was formerly termed a stere. A cubic
centimeter is essentially the same as a milliliter.

Traditional US measures of volume:

   * US fluid ounce, about 29.6 ml (this volume of water weighs one ounce)
   * US pint = 16 ounces, or about 473 ml (this volume of water weighs one
     pound)
   * US quart = 32 ounces or two pints, or about 946 ml
   * US gallon = 128 ounces or four quarts, about 3.785 l

Traditional UK measures of volume:

   * UK fluid ounce, about 28.4 ml (weight of this volume of water is 28.3
     g, or nearly one ounce, 28.4 g)
   * UK pint = 20 fluid ounces, or about 568 ml
   * UK quart = 40 ounces or two pints, or about 1.136 l
   * UK gallon = 160 ounces or four quarts, or about 4.546 l

Traditional cooking measures for volume also include:

   * teaspoon = 1/6 ounce
   * tablespoon = 1/2 ounce or 3 teaspoons
   * cup = 8 ounces or 1/2 pint

To help compare different volumes, see these pages:

   * 10 cm3 -
   * 100 cm3 -
   * 1.0 dm3 -
   * 10 dm3 -
   * 0.1 m3 -
   * 1.0 m3 -
   * 10 m3 -
   * 100 m3 -
   * 1,000 m3 -
   * 10,000 m3 -
   * 100,000 m3 -