Volume Formulas

Volume of a cube:

s = length of a side

Volume of a rectangular prism:

l = length, w = width, h = height

Volume of a cylinder (circular prism):

r = radius of circular face, h = distance between faces

Any prism that has a constant cross sectional area along the height volume:

A = area of the base, h = height

Volume of a sphere:

r = radius of sphere
which is the first integral of the formula for Surface Area of a sphere

An ellipsoid volume :

a, b, c = semi-axes of ellipsoid

Volume of a pyramid:

A = area of base, h = height from base to apex

Volume of a cone

(circular-based pyramid):

r = radius of circle at base, h = distance from base to tip

Any figure volume (calculus required)

h = any dimension of the figure, A(h) = 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).