Geometry/Volume

Volume

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

Common equations for volume:
Shape	Equation	Variables
A cube:	$s^3=s\cdot s\cdot s$	s = length of a side
A rectangular prism:	$l\cdot w\cdot h$	l = length, w = width, h = height
A cylinder (circular prism):	$\pi r^2\cdot h$	r = radius of circular face, h = height
Any prism that has a constant cross sectional area along the height:	$A\cdot h$	A = area of the base, h = height
A sphere:	$\frac{4}{3}\pi r^3$	r = radius of sphere which is the integral of the Surface Area of a sphere
An ellipsoid:	$\frac{4}{3}\pi abc$	a, b, c = semi-axes of ellipsoid
A pyramid:	$\frac{1}{3}Ah$	A = area of the base, h = height of pyramid
A cone (circular-based pyramid):	$\frac{1}{3}\pi r^{2}h$	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)