This page gives a reference to some of the formulas to find out volumes of basic shapes.
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
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 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 |
| Tetrahedron |
V = a3⁄ (6 √2)
| a = length of the edge |
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