Volume Formulas

Volume is the space occupied by an object or a shape that has three dimensions. It is measured in cubic units mostly. In other words, the volume of any object or vessel is the vessel's ability to carry the volume of fluid, be it in a gaseous state or in a liquid state. The volumes of three-dimensional mathematical shapes such as cube, cuboid, cylinder, prism, and cone etc can be calculated easily using arithmetic formulas. However, for more complicated shapes, integral calculus is required to obtain their volume.

For example, we can see how the volume of a cylinder is determined as: 

where r = d⁄2.

• r = radius of the circular base

• d = Diameter of the circular base

• h = Cylinder height

Formulae of Various Geometrical Figures for Volume

Some of the formula to compute the volumes of some of the basic shapes are written as under:-

• Rectangular Solid or Cuboid  V = l × w × h

              where ,

 l = Length

  w = Width

  h = Height

• Cube:

Where 

a = Edge length or side

• Cylinder:  

Where

 r = Radius of the circular base

           h = Height 

•  Prism:  V = B × h 

  B = Base area, (B = side2 or length.breadth)

              h = Height

• Sphere :

Where

r = Radius of the sphere

• Pyramid\\tV = (1/3) × B × h

Where,

B = Area of the base,

           h = Height of the pyramid

• Right Circular Cone: 

r = Radius of the circular base

           h = Height

• Square or Rectangular Pyramid\\tV = (1/3) × l × w × h

Where

l = Length of the base,

         w = Width of base

          h = Height (base to tip)

• Ellipsoid V = (4/3) × π × a × b × c

Where


a, b, c = semi-axes of an ellipsoid

• 
Tetrahedron
V = a3 ⁄ (6√2)

where


a = Length of the edge

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