PEAZIT Aha card
Go straight to resources ↓A sector is a fraction of a whole circle
A sector of α degrees occupies α/360 of the circle. The same fraction applies to its arc.
| Relation | Meaning |
|---|---|
| f = 90° / 360° = 1/4 | 90° is one quarter of a full turn. |
| S = f × πr² | Multiply the whole area by this fraction. |
| r = 4; S ≈ 12.56 cm² | One quarter of 3.14 × 16 is 12.56. |
One worked example
- f = 90° / 360° = 1/490° is one quarter of a full turn.
- S = f × πr²Multiply the whole area by this fraction.
- r = 4; S ≈ 12.56 cm²One quarter of 3.14 × 16 is 12.56.
Watch out: The formula α/360 uses degrees. Arc length is not sector perimeter: the latter includes two radii.
Goal, prerequisites and card origin
What you will learn: Use the central angle as a fraction of a full turn.
What you need first: Circle area, circumference and fractions.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
A sector of α degrees occupies α/360 of the circle. The same fraction applies to its arc.