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For any given solid object, the space occupied by such an object is measured and is termed as the volume of the object. Also, if the object is hollow, then the interior is known to be empty. The hollow part can be filled with air or some liquid. In this case, the volume of the substance that can fill the interior will give the capacity of any container.
Therefore, the volume of an object can be defined as the measure of the space it occupies or the capacity of an object is the volume of substance its interior can accommodate. Here, the unit of measurement of either of the two is cubic unit.
Units of Volume
Volume is measured in “cubic” units. The volume of any given figure is the number of cubes required to fill it completely, for example, blocks in a box.
The volume of a cube equals side x side x side. Since each side of a square is equal, it can simply be the length of one side cubed.
If suppose a square has one side of 4 inches, the volume would be 4 inches times 4 inches x 4 inches, or 64 cubic inches. (Cubic inches can also be written in3.)
Some of the formulas to find out volumes of basic geometrical shapes are –
Formulas of Volume of Various Figures
|
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 = π r2h |
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)π r3 |
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 |
Solved Examples
Question 1) The dimensions of a rectangular water tank are given as 2m 75cm, 1m 80cm, and 1m 40cm. How many liters of water can be filled in the tank of given measurements?
Solution) As we know that 1m = 100cm.
Dimensions of the tank are given as 2m 75cm, 1m 80cm, and 1m 40cm.
We can write this as 275cm, 180 cm, 140 cm
Now, we know that the volume of the cuboid is, Volume = l × b × h
V = 275 × 180 × 140
V = 6930000 cm3
Since 1000 cm = 1 Liter
Thus, V = 6930 liters
Hence the tank can hold 6930 liters of water.