 # Volume Formulas

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. 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 using the formula πr2h, where r = d⁄2.

• r = Radius of the circular base
• d = Diameter of the circular base
• h = Height of the 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 base

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

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 an ellipsoid
Tetrahedron V = a3⁄ (6 √2) a = Length of the edge

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 More topics in Volume Formula Volume of a Cube Formula Spherical Cap Volume Formulas

#### 1 Comment

1. Thank You! Helped me with my math project!