1. Understanding a Cuboid
A cuboid is a 3D solid with six rectangular faces. It has three dimensions:
- Length \(l\)
- Breadth \(b\)
- Height \(h\)
Everyday examples include rooms, bricks, books, boxes, and water tanks. The volume of a cuboid tells us how much space it encloses.
2. Formula for Volume of a Cuboid
To understand the formula, imagine filling the cuboid with small unit cubes of side 1 cm. The number of such cubes equals the cuboid's volume.
Since the cuboid extends:
- \(l\) units along length,
- \(b\) units along breadth,
- \(h\) units along height,
The volume is simply the product of the three dimensions:
\( \text{Volume} = l \times b \times h \)
2.1. Example
A cuboid has length \(l = 10\,\text{cm}\), breadth \(b = 6\,\text{cm}\), and height \(h = 4\,\text{cm}\). Then:
\( \text{Volume} = lbh = 10 \times 6 \times 4 = 240\,\text{cm}^3 \)
This means the cuboid can hold 240 cubic centimetres of space.
3. Why the Formula Makes Sense
Think of the cuboid as being built layer by layer:
- Each layer covers an area of \(l \times b\)
- There are \(h\) such layers stacked vertically
Total space:
\( (l \times b) \times h = lbh \)
This is why volume depends on the product of all three dimensions.
4. Real-Life Applications
The volume of a cuboid is used in many practical situations:
- Finding capacity of water tanks, aquariums, or storage boxes
- Calculating space inside rooms or cupboards
- Packaging and shipping calculations
- Determining material needed to construct solid rectangular blocks
Whenever you need the internal space of a box-like structure, use the formula \(lbh\).