Which question, which measure
One drum, and two orders arrive the same morning. One order asks for tin sheet to cover it. The other asks for oil to fill it.
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- One drum, two questions.
- Tin sheet covers it — square units.
- Oil fills it — cubic units.
- Some jobs need both answers. A rope needs a length.
The rule
Covering or wrapping wants a surface area, in square units. Filling wants a volume, in cubic units. A rope or strip wants a length.
Take a drum, a cylinder like a tin. Its radius r is 7 cm. Its height h is 10 cm. Use π ≈ 22/7.
Tin sheet is the curved surface plus both ends. The curved surface is 2πr × h = 44 × 10 = 440 cm². One end is πr² = 154 cm². Both ends make 2 × 154 = 308. So the sheet is 440 + 308 = 748 cm².
Oil is the volume: 154 × 10 = 1540 cm³.
| Job | Kind of answer | Number |
|---|---|---|
| New label for the drum | surface | 440 cm² |
| Oil the drum holds | volume | 1540 cm³ |
| Wrapping for an 8 cm by 5 cm by 3 cm carton | surface | 158 cm² |
| Grain filling that carton | volume | 120 cm³ |
| Canvas for a tent with a 6 m square base, 4 m high | surface | 60 m² |
| Paint for the closed drum | surface | 748 cm² |
| Rope round the drum's rim | length | 44 cm |
The same drum needs different measures for different jobs. Ask what the job needs: a skin, a filling or a line. A skin is a surface area. A filling is a volume. A line is a length.
A litre is 1000 cm³. So 1540 cm³ is 1540 ÷ 1000 = 1.54 litres.
1 m is 100 cm. So 1 m² is 100 × 100 = 10000 cm². And 1 m³ is 100 × 100 × 100 = 1000000 cm³.