Concept 1 · free preview
Area, volume and units
Understand
Perimeter = length of the boundary (m, cm). Area = flat space covered (m², cm²). Volume = space inside a solid (m³, cm³). Before calculating, bring every length to the same unit.
| Conversion | Value |
|---|---|
| 1 m | 100 cm |
| 1 m² | 100 × 100 = 10,000 cm² |
| 1 m³ | 100 × 100 × 100 = 1,000,000 cm³ |
| 1 litre | 1,000 cm³ |
| 1 m³ | 1,000 litres |
| 1 hectare | 10,000 m² |
Rule
Number of tiles = floor area ÷ area of one tile (both in the same unit)
Length of carpet = floor area ÷ width of the carpet
Cost = quantity × rate (note whether the rate is per m, m² or m³)
Example
Tiles of 50 cm × 40 cm on a 5 m × 4 m floor: along the length 500 ÷ 50 = 10, along the width 400 ÷ 40 = 10 → 10 × 10 = 100 tiles.
Example
A 6 m × 5 m room, carpet 50 cm (= 0.5 m) wide at ₹20 per metre: length of carpet = 30 ÷ 0.5 = 60 m → cost = 60 × 20 = ₹1,200.
Common mistake
Assuming 1 m² = 100 cm². Area converts twice: 1 m² = 10,000 cm².
Check yourself
How many litres of water does a 2 m × 1.5 m × 1 m tank hold?