What is cube?
Cube is a 3D shape of a square.
The Cube has 6 square faces, 8 vertices and 12 edges.
Like square, all the sides of cube are equal in length and all the vertices angle measures 90 degree
Features of Cube
(a) 3D shape of square
(b) 6 Square faces
(c) All sides are equal in length
Example of Cube
Rubik’s cube is one of the most common example of cube found in dailylife.
What is Volume of Cube?
Volume of cube is the amount of space captured inside the cube.
Consider the cubic aquarium above.
The volume of water used to fill the aquarium to brink is equal to the volume of the cube.
Hence, the total space captured by the cube is called volume of cube.
In the above figure, the empty space is filled with air, but you can use it to fill it with water.
Volume of Cube Formula
The formula for volume of cube is:
Volume = Length x Breadth x Height
We know that in cube, side lengths are same
Let side = a
\mathtt{V\ =\ a^{3}}
Cube Volume – Formula Explanation
The formula for volume of cube is;
Volume of cube = Side x Side x Side
Let us understand the formula step by step:
Step 01
When we multiply Side x Side, we get area of one face of square
Step 02
When we include third side in the formula, we introduce new dimension in the cube
You can see that third dimension is included backwards to make the figure three dimensional.
That’s how we get formula;
Volume = Side x Side x Side
Unit of Volume
The volume of cube (or any object) is measured in cubic units
Explanation
Given above is the cube of side a meter
Volume of cube
= Length x Breadth X Height
= a meter x a meter x a meter
= \mathtt{Volume\ =a^{3} \ m^{3} \ }
See that the volume is expressed in \mathtt{m^{3} \ } {cubic units}
Infact, whenever you see any data with units like \mathtt{\ m^{3} ,\ cm^{3} \ } etc. , make a note that data is about the volume
Finding length of cube using volume data
How to find side length of cube when volume data is given?
The method is very simple.
Let the volume of cube given is V
We know that:
Volume of Cube = Length x Breadth x Height
We also know that;
In cube, the length of all sides are equal
Let the side length be a
Now the formula becomes
\mathtt{V=\ a\ \times a\ \times \ a}\\\ \\ \mathtt{V\ =\ a^{3}}\\\ \\ \mathtt{a\ =\ \sqrt[3]{V}}
Example
The volume of cube is 512 \mathtt{( cm)^{3}}\ . Find the side length of the cube.
Given:
Volume of cube (V) = 512 \mathtt{( cm)^{3}}\\\ \\
\mathtt{We\ have\ seen\ that}\\\ \\ \mathtt{Side\ =\ \sqrt[3]{V}}\\\ \\ \mathtt{Putting\ the\ value\ of\ V}\\\ \\ \mathtt{Side\ =\sqrt[3]{512\ cm^{3}}}\\\ \\ \mathtt{Side\ =\ 8\ cm}
Finding Volume of cube when total surface area is given
What is total surface area of cube?
We know that cube is made by joining six squares of equal sides
Area of 1 Face = \mathtt{a\ \times a\ =\ a^{2}}
Total Surface Area of Cube = Area of 6 Face
S = \mathtt{6\ a^{2}}\
When total surface area of cube is given, you can find volume of cube using following steps:
Step 01
Find the side length using total surface Area
Let S be total surface area
\mathtt{S\ =\ 6\ a^{2}}\\\ \\ \mathtt{a\ =\ \sqrt{\frac{S}{6}}}
Step 02
Now find volume of cube using formula
\mathtt{Volume\ =\ ( a)^{3}}
Volume of cube questions
(01) Find the volume of cube of side 3 meter
Given
Side of cube (a) = 3 meter
\mathtt{we\ know\ that}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( a)^{3}}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( 3)^{3} \ =\ 27\ m^{3}}
Hence, 27 \mathtt{m^{3}} is the solution
(02) The total surface area of cube is 24 sq. cm. Find the volume of cube
Given
Surface area of cube = 24 sq cm
\mathtt{We\ know\ that}\\\ \\ \mathtt{Surface\ area\ of\ cube\ =\ 6\ a^{2}}\\\ \\ \mathtt{24\ =\ 6\ a^{2}}\\\ \\ \mathtt{a^{2} \ =\ 4}\\\ \\ \mathtt{a\ =\ 2\ cm}
Hence side length of cube is 2 cm
Now let us find the volume of cube;
\mathtt{we\ know\ that}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( a)^{3}}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( 2)^{3} \ =\ 16\ cm^{3}}
(03) Find the volume of below cube
Given
Side length (a) = 10 meter
We know that in cube all sides are equal
Formula for Volume of cube is;
\mathtt{Volume\ of\ cube\ =\ ( a)^{3}}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( 10)^{3} \ =\ 1000\ m^{3}}