Theory:

Cube:
Cube is a special type of cuboid whose length, breadth and height are all equal.
Volume of a cube:
Let \(a\) be the edge length of the cube.
 
cube_vol.png
 
Volume of a cuboid \(=\) \(lbh\) cu. units.
 
For a cube, length \(=\) breadth \(=\) height \(=\) edge
 
That is, \(l\) \(=\) \(b\) \(=\) \(h\) \(=\) \(a\)
 
Substitute this in the volume of a cuboid formula.
 
Volume of a cuboid \(=\) \(a \times a \times a\) \(=\) \(a^3\) \(=\) Volume of a cube
 
Therefore, the volume of a cube \(=\) \(a^3\) cu. units.
Example:
The edge of the cubical tank is \(5\) \(m\). Find how much water it holds in litres?
 
\([\)Hint: \(1 \ m^3 = 1000 \ l]\)
 
Solution:
 
Edge of the cubical tank \(=\) \(5\) \(m\)
 
Volume of the cubical tank \(=\) \(a^3\)
 
\(=\) \(5^3\)
 
\(=\) \(5 \times 5 \times 5\)
 
\(=\) \(125\) \(m^3\)
 
Now, convert \(m^3\) to \(l\).
 
\(1 \ m^3 = 1000 \ l\)
 
\(125 \ m^3 = 125 \times 1000 = 125000\)
 
Therefore, the volume of the cubical tank is \(125000 \ l\).
Important!
For any two cubes:
 
1. \(\text{Ratio of surface areas}\) \(=\) \((\text{Ratio of sides})^2\)
 
2. \(\text{Ratio of volumes}\) \(=\) \((\text{Ratio of sides})^3\)
 
3. \((\text{Ratio of surface areas})^3\) \(=\) \((\text{Ratio of volumes})^2\)