Geometry/Volume
Volume[edit]
Volume is like area expanded out into 3 dimensions. Area deals with only 2 dimensions. For volume we have to consider another dimension. Area can be thought of as how much space some drawing takes up on a flat piece of paper. Volume can be thought of as how much space an object takes up.
Volume formulae[edit]
Common equations for volume:  

Shape  Equation  Variables 
A cube:  s = length of a side  
A rectangular prism:  l = length, w = width, h = height  
A cylinder (circular prism):  r = radius of circular face, h = height  
Any prism that has a constant cross sectional area along the height:  A = area of the base, h = height  
A sphere:  r = radius of sphere which is the integral of the Surface Area of a sphere 

An ellipsoid:  a, b, c = semiaxes of ellipsoid  
A pyramid:  A = area of the base, h = height of pyramid  
A cone (circularbased pyramid):  r = radius of circle at base, h = distance from base to tip
. 
(The units of volume depend on the units of length  if the lengths are in meters, the volume will be in cubic meters, etc.)
Pappus' Theorem[edit]
The volume of any solid whose cross sectional areas are all the same is equal to that cross sectional area times the distance the centroid(the center of gravity in a physical object) would travel through the solid.
Image:PappusCentroidTheoremExample.jpg
Cavalieri's Principle[edit]
If two solids are contained between two parallel planes and every plane parallel to these two plane has equal cross sections through these two solids, then their volumes are equal.