A slice of the inside
Two radii and an arc mark out a slice of a circle.
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Step 1 of 4
- A circle. Its inside area is 154.
- A 90° sector is shaded.
- The sector is 1/4 of the area.
- 1/4 of 154 is 38.5. Sector area = 38.5.
The rule
Sector — the region between two radii and the arc that joins them.
Rule: A sector's area is a share of the circle's area. The share is the angle's share of a turn.
The angle is the one at the centre, between the two radii. The circle's area is π × r × r.
| Angle at centre | Share of the turn | Sector area |
|---|---|---|
| 45° | 1/8 | 19.25 |
| 90° | 1/4 | 38.5 |
| 180° | 1/2 | 77 |
| 360° | 1 (the whole turn) | 154 |
m² means square metres. A sprinkler throws water 14 m. It turns through 60°. So the water covers a sector of radius 14 m. The full circle has area 22/7 × 14 × 14 = 616 m². The water covers 60/360 = 1/6 of that. 616 × 60/360 = 102.67 m², rounded.
Watch out!
A sector is not its arc. An arc is a length, in units. A sector is an area, in square units.