History of Volume

	Revision 16 . . (edit) November 21, 2001 12:15 am by LA2
	Revision 15 . . (edit) November 21, 2001 12:13 am by LA2
	Revision 14 . . (edit) August 29, 2001 6:45 am by Lee Daniel Crocker
	Revision 9 . . (edit) August 17, 2001 6:30 am by (logged).176.164.xxx [*fixed note: to no longer appear as though it's in the list]

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Difference (from prior major revision) (minor diff, author diff)

Changed: 1c1

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.

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.

Changed: 6,11c6,11

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)

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)

Changed: 14c14

-> **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!)

-> **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).

Changed: 17c17,31

A commonly used SI unit for volume is the liter, and one thousand liters is the volume of a cubic meter.

A commonly used SI unit for volume is the liter, and one thousand liters is the volume of a cubic meter. 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]? -