Volume is the total space occupied by the three-dimensional solid figure. In this article, we are going to find the Volume of cube with different dimensions like cm, m, inches, and so on. In a cube all the sides are equal. You can learn how to calculate the volume of the cube with formulas from here. Also, you can find examples of the volume of a cube with explanations.
What is the Volume of a Cube?
The definition of volume of a cube is the total number of cubic units occupied by the cube. The units of volume of a cube are cubic units. A cube is a three-dimensional geometric figure with 6 faces and sides. The length, breadth, and height of a cube are equal.
So, the volume of a cube is a × a × a
The Volume of Cube Formula
The volume of cube = s × s × s (or) s³
Where
s is the side of the cube
The Volume of Cube using Side Formula
The volume of a cube can be measured by multiplying the lengths of the cube. The dimensions of the cube are length, breadth and height. We have to multiply all three dimensions to find the volume of a cube. All the sides in a cube are the same.
So, the volume of a cube using side is a × a × a cubic units
The Volume of Cube using Diagonal Formula
The volume of a cube whose diagonal (d) is √3a, where, ‘a’ is the side length of the cube.
V = [√3×(diagonal)³]/9
How to Find the Volume of a Cube?
The volume of a cube can be found by using the formulas. There are two formulas to calculate the volume of a cube. One is using the edge length and the other is using the measure of its diagonal.
The Volume of Cube using edge length
The lengths of the cube are equal. The steps to find the volume of a cube using the edge length is shown here.
step 1: First check out the measure of the given cube.
step 2: Apply the volume of a cube formula to find the measure of the cube.
Volume = a × a × a
step 3: Note down the obtained value and write the units of the volume.
The Volume of Cube using Diagonal
We can find the volume of a cube using the diagonals of the figure. Read the below steps to know how to find the volume of a cube using the diagonals.
step 1: Note down the measurements of the given cube.
step 2: Apply the volume of a cube using a diagonal formula to find the measure of the cube.
[√3×(diagonal)³]/9
step 3: Write down the obtained value with the units of the volume.
See More:
Volume of a Cube Word Problems with Solutions
Solve the given problems to test your math skills on the topic volume of a cube.
Example 1.
Using the volume of a cube formula, calculate the side length of a Rubik’s cube whose volume is 125 in³.
Solution:
Given that,
The volume of Rubik’s cube = 125 in³
Using the volume of a cube formula
The volume of the cube = s³
where ‘s’ is the side length.
Putting the values, we get,
125 = (s³)
s = (125)¹/³ = 5 in
Therefore, the Side length of the Rubik’s cube = 5 in.
Example 2.
Find the volume of a cube if the length of its diagonal is 6 inches?
Solution:
Given that
Diagonal of the cube = 6 in.
Using the volume of a cube formula,
The volume of the cube when diagonal is given
Volume of cube = (√3×d3)/9
d³ = 6 × 6 × 6 = 216
Volume of given cube = (√3×216)/9 = 41.5 in³
Therefore, Volume of the cube = 41.5 in³
Example 3.
The volume of a cube is 27cm³, then what is the measure of the edge of a cube?
Solution:
Given that
Volume of a cube = V = 27 cm³
We know that, V = (side)³ or (edge)³
(edge)³ = 27 = 3³
Therefore, edge of the cube = 3 cm
Example 4.
What is the volume of a cube of 5 cm?
Solution:
Given that
Side of the cube = a = 5 cm
We know that
The volume of a Cube formula is V= a³
Volume of a cube = 5³ cm³
Therefore the volume of a cube is 125 cm³
Example 5.
What is the volume of a cube of 10 cm?
Solution:
Given that
Side of the cube = a = 10 cm
We know that
The volume of a Cube formula is V= a³
V= 10³ cm³
Therefore V = 1000 cm³
FAQs on Volume of a Cube
1. What is the formula of the volume of the cube?
The formula of volume of the cube is given by:
Volume = a³, where a is the length of its sides or edges.
2. What is the unit of volume of a cube?
The unit of volume of a cube is given by cubic units or unit³, such as cm³, m³, in³, and so on.
3. What is meant by the volume of a cube?
The volume of a cube is the space occupied by the three-dimensional shape.