Units & Dimensions - VOLUME
VOLUME OF CUBE
The volume of a cube defines the number of cubic units that are occupied by the cube completely. A cube is a solid three-dimensional figure, which has 6 square faces or sides. To calculate the volume we should know the dimensions of the cube.
Volume of Cube Formula
We can easily find the volume of the cube (V), by knowing the length of its edges. Suppose, the length of the edges of the cube is ‘a’. Then the V will be the product of length, height, and width. So, the volume of the cube formula is
Volume of a Cube = Length × Width × Height
V = a × a × a= a3
where ‘a’ is the length the side of cube or edges.
Derivation for Volume of a Cube
The volume of an object is defined as the amount of space a solid occupies. We know that a cube is a 3-dimensional object whose all the sides i.e. length, breadth, and height are equal. Now for a cube, the volume derivation will be as follows:
· Consider a square sheet of a paper.
· Now, the area that the square sheet will take up will be its surface area i.e. its length multiplied by its breadth.
· As the square will have equal length and breadth, the surface area will be “a2”.
· Now, a cube is made by stacking multiple square sheets on top of each other so that the height becomes “a” units. This gives the height or thickness of the cube as “a”.
· Now, it can be concluded that the overall area covered by the cube will be the area of the base multiplied by the height.
· So, Volume of Cube = a2 × a = a3
SOLVED EXAMPLES
Example 1: Find the volume of the cube, having the sides of length 7 cm.
Solution:
Given, the length of sides of the cube is 7cm.
We know, Volume of a cube = (length of sides of the cube)3
Therefore, Volume, V = (7 cm)3= 343 cm3
Example 2: Find the length of the edges of the cube, if its volume is equal to 125cm3.
Solution:
Given, Volume of the cube = 125 cm3
Let the length of the edges is a.
We know, by the formula,
The volume of a cube = (length of edges of the cube)3
Substituting the value, we get,
125 = a3
\(a = \sqrt[3]{{125}}\) = 5 cm
Therefore, the length of the cube is 5cm.