Volume Formulas
| Shape | Volume formula | Variables |
|---|---|---|
| Cube | a = length of any side (or edge) | |
| Cylinder | r = radius of circular face, h = height | |
| Prism | B = area of the base, h = height | |
| Rectangular prism | l = length, w = width, h = height | |
| Sphere | r = radius of sphere which is the integral of the surface area of a sphere |
|
| Ellipsoid | a, b, c = semi-axes of ellipsoid | |
| Pyramid | B = area of the base, h = height of pyramid | |
| Cone | r = radius of circle at base, h = distance from base to tip or height | |
| Tetrahedron | edge length | |
| Parallelepiped | 
|
a, b, and c are the parallelepiped edge lengths, and α, β, and γ are the internal angles between the edges |
| Any volumetric sweep (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. a and b are the limits of integration for the volumetric sweep. (This will work for any figure if its cross-sectional area can be determined from h). |
|
| Any rotated figure (washer method) (calculus required) |
and are functions expressing the outer and inner radii of the function, respectively. | |
| Klein bottle | No volume—it has no inside. |
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Unmixed with baser matter.”
—William Shakespeare (1564–1616)
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