Foundation and Higher · arcs and sectors
Arcs and sectors
are just fractions
of a circle.
find the fraction,
the rest is easy
first, the word itself —
Sector
Latin secare — to cut
a slice cut from the centre
step 1 of 3
What fraction?
1. The angle at the centre is 60°.
2. A full turn is 360°, so six of these
slices fit in the circle.
✓ Fraction = 60 ÷ 360 = 1/6
step 2 of 3
Arc length
1. Whole circumference: 2 × π × 6 = 12π cm.
2. The arc is 1/6 of it.
✓ Arc length = 1/6 × 12π = 2π cm
= 6.28 cm
step 3 of 3
Sector area
1. Whole circle: π × 6² = 36π cm².
2. The sector is 1/6 of it.
✓ Sector area = 1/6 × 36π = 6π cm²
= 18.8 cm²
fraction first, then the formula —
Arc length
fraction × circumference
Sector area
fraction × area of the circle
An arc is a length: cm.
A sector is an area: cm².
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