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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:
math geometry cube volume formula
s = length of a side
Volume of a rectangular prism:
math geometry rectangular prism volume formula
l = length, w = width, h = height
Volume of a cylinder (circular prism):
maths geometry cylinder(circular prism) volume formula
r = radius of circular face, h = distance between faces
Any prism that has a constant cross sectional area along the height volume:
math geometry any prism with constant cross sectional area along the height volume formula
A = area of the base, h = height
Volume of a sphere:
maths geometry sphere volume formula in math
r = radius of sphere
which is the first integral of the formula for Surface Area of a sphere
An ellipsoid volume :
math geometry ellipsoid volume formula
a, b, c = semi-axes of ellipsoid
Volume of a pyramid:
math geometry pyramid volume formula
A = area of base, h = height from base to apex

Volume of a cone

(circular-based pyramid):

maths geometry cone volume formula
r = radius of circle at base, h = distance from base to tip
Any figure volume (calculus required)
math geometry any figure volume formula
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).



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