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# Volume Formulas

Geometry volume formulas of a cube, sphere, rectangular prism, pyramid, cylinder, ellipsoid, cone, any prism that has a constant cross sectional area along the height, and a general volume formula for any figure.

Shape
Formula
Variables
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:
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).