### 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.

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. $$(\text{Ratio of surface areas})^3$$ $$=$$ $$(\text{Ratio of volumes})^2$$