Volume Formulas

The volume of an object is the amount of space occupied by the object, which is three dimensional in shape. It is usually measured in terms of cubic units. In other words, the volume of any object or container is the capacity of the container to hold the amount of fluid (gas or liquid). The volume of three-dimensional mathematical shapes like cube, cuboid, cylinder, prism and cone etc. can be easily calculated by using arithmetic formulas. Whereas, to find the volumes of complicated shapes, one can use integral calculus.

For example, the volume of the cylinder can be measured as = πr2h, where r = d⁄2

  • r = radius of the circular base
  • d = Diameter of the circular base
  • h = height of the cylinder

Volume Formula of Cylinder

Volume Formulas of Various Geometric Figures

Some of the formulas to find out volumes of basic shapes are –

Shapes Volume Formula Variables
Rectangular Solid or Cuboid V = l × w × h

l = Length,

w = Width,

h = Height

Cube V = a3 a = length of edge or side
Cylinder V = πr2h

r = radius of the circular edge,

h = height

Prism V = B × h

B = area of base, (B = side2 or length.breadth)

h = height

Sphere V = (4⁄3)πr3 r = radius of the sphere
Pyramid V = (1⁄3) × B × h

B = area of the base,

h = height of the pyramid

Right Circular Cone V = (1⁄3)πr2h

r = radius of the circular base,

h = height (base to tip)

Square or Rectangular Pyramid V = (1⁄3) × l × w × h

l = length of the base,

w = width of base,

h = height (base to tip)

Ellipsoid V = (4⁄3) × π × a × b × c a, b, c = semi-axes of ellipsoid

V = a3⁄ (6 √2)

a = length of the edge

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