1. Understanding Volume of a Cube
A cube is a 3D shape with all edges equal in length. Each face is a square of side \(a\).
The volume of a cube tells us how much space is inside it. In simpler terms, it measures the capacity or the amount of material (like water, sand, or air) the cube can hold.
2. Formula for Volume of a Cube
To find the volume of a cube, imagine filling it with small unit cubes (each of size 1 × 1 × 1). The total number of such cubes gives its volume.
Since each dimension—length, breadth, and height—is \(a\):
\( \text{Volume} = a \times a \times a = a^3 \)
2.1. Example
If a cube has side length \(a = 6\,\text{cm}\), then its volume is:
\( a^3 = 6^3 = 216\,\text{cm}^3 \)
This means the cube can hold 216 cubic centimetres of space.
3. Visual Understanding
You can imagine a cube as built from layers of square tiles:
- Each layer has \(a \times a\) small cubes
- There are \(a\) such layers stacked
So, total small cubes:
\( a \times a \times a = a^3 \)
This helps you visualise why the volume formula involves cubing the side.
4. Real-Life Applications
The volume of a cube is used in many situations, such as:
- Finding the capacity of a cubic tank or container
- Calculating storage space in boxes
- Designing dice, Rubik’s cubes, and packaging
- Understanding how much material is needed to make solid cube blocks
Any time you need to measure the internal space of a perfect cube, use \(a^3\).