A piece of the edge
Show on a big screenA cycle wheel has spokes. Two neighbouring spokes mark a piece of the rim. The rim is the wheel's outer edge.
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- A circle. Its way round is 44.
- Two radii make 90° at the centre.
- The arc between them is 1/4 of the turn.
- 1/4 of 44 is 11. Arc length = 11.
The rule
An is a share of the way round. The share is the angle's share of a turn.
Arc — a piece of the rim between two radii.
length = way round × angle ÷ 360. The angle is the one at the centre, in degrees. For radius r, the way round is 2πr.
| Angle at centre | Share of the turn | Arc (way round = 44) |
|---|---|---|
| 0° | 0 | 0 |
| 60° | 1/6 | 7.33 |
| 90° | 1/4 | 11 |
| 180° | 1/2 | 22 |
| 360° | 1 (the whole turn) | 44 |
A zero angle takes no share, so its has length 0. A full turn takes the whole share. Its arc is the whole way round.
The of a semicircle is half the way round: πr. The arc of a quarter circle is πr/2.
A wheel has 12 equally spaced spokes. They cut the turn into 12 pieces. Each pair of neighbouring spokes makes 360 ÷ 12 = 30° at the centre. So each is 30/360 = 1/12 of the way round.
A slice of the circle has two straight edges, the radii. Its perimeter is the plus two radii. Take radius 21 and angle 40°. The way round is 2 × 22/7 × 21 = 132. The arc is 132 × 40/360 = 14.67, rounded. The perimeter is 14.67 + 21 + 21 = 56.67.
Try the lab to finish this lesson.