Volume of a Box
Volume of a rectangular cuboid.
Formula
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Example
A 2 × 3 × 5 box: V = 2·3·5 = 30 cubic units.
How it works
For a rectangular box, the volume tells you how much space fits inside it. The formula V = lwh works because you can think of the box as being built from layers: first find the area of the base (length × width), then multiply by the height to count how many of those layers fit. The result is measured in cubic units because you are measuring space in three dimensions.
When to use it
Use this formula whenever you need the space inside a rectangular container or prism, such as a storage box, aquarium, shipping carton, or room shaped like a rectangular prism. It is also useful in geometry problems that ask for the capacity of a cuboid.
Worked example, step by step
A rectangular fish tank is 8 cm long, 4 cm wide, and 6 cm high. V = l × w × h V = 8 × 4 × 6 V = 32 × 6 V = 192 So, the volume is 192 cubic centimeters.
Common mistakes to avoid
- Adding the three dimensions instead of multiplying them
- Forgetting to use cubic units, such as cm³ or m³
- Mixing up width and height or using the wrong measurement units
Did You Know?
The rectangular box volume, length×width×height, is the 3-D extension of area.
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