Question
A rectangular box (cuboid) has length = 12 cm, breadth = 8 cm, and height = 5 cm. Find its volume.
Solution — Step by Step
The volume of a cuboid is the space it occupies in three dimensions. We multiply all three dimensions together:
From the problem:
- Length cm
- Breadth cm
- Height cm
Do it in two steps to avoid errors: , then .
Volume is always in cubic units. Since our dimensions are in cm:
Why This Works
Think of the cuboid as a stack of identical rectangular sheets. Each sheet has area . We’re stacking such sheets on top of each other — so total volume is .
This is why the unit becomes cm³ (centimetres cubed) — we’re multiplying three lengths, so the units multiply too: cm × cm × cm = cm³.
Where = length, = breadth, = height. All dimensions must be in the same unit before multiplying.
Alternative Method — Using Area of Base
Sometimes the question gives you the base area directly instead of and separately.
If base area and height cm:
Same answer. This method is handy when the question says “a cuboid with base area 96 cm² and height 5 cm” — you skip one multiplication step.
Common Mistake
Forgetting to cube the unit. Students often write the answer as 480 cm instead of 480 cm³. Volume is always in cubic units — cm³, m³, mm³. Writing 480 cm is a length, not a volume. In board exams, the unit carries marks separately, so never skip it.
Mixed units trap: If m, cm, cm — convert everything to the same unit first. Most students get caught here in Class 8 word problems. Convert to cm: cm, then multiply. The answer in cm³ can be converted to litres if needed: 1 litre = 1000 cm³.
This formula carries forward directly into Class 9 and 10 surface area chapters, and the same logic underlies cylinder and cone volume in Class 10. Getting comfortable with now makes that transition easy.