A tin unrolled
Peel the label off a tin, and it lies flat.
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Step 1 of 4
- A cylinder, radius r, height h.
- Mark the seam, where the label joins.
- Peel the curved side off.
- It unrolls flat: width 2πr, height h.
The rule
A cylinder has two round ends and a curved side. The rim is the round edge of an end. The label wraps once round the rim.
The circumference is the distance round a circle. So the label's length is the circumference, 2πr.
The radius r is the distance from the centre to the rim. The height h is the distance between the two ends.
curved surface = 2πr × h
total surface = 2πr × h + 2 × πr²
volume = πr² × h
π is a fixed number, a little more than 3. Here π ≈ 22/7, and every calculation uses that. The sign ≈ means almost equal to.
Take a tin with r = 7 cm and h = 10 cm.
| Question | Working | Answer |
|---|---|---|
| Label length | 2 × 22/7 × 7 | 44 cm |
| Curved surface | 44 × 10 | 440 cm² |
| One end | 22/7 × 7 × 7 | 154 cm² |
| Total surface | 440 + 2 × 154 | 748 cm² |
| Volume | 154 × 10 | 1540 cm³ |
The volume is the end area times the height: 154 × 10.