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How to calculate the unknown among a central angle, radius, and arc length of a given circle
Find the length of the arc in terms of π that subtends an angle of 30∘ at the centre of a circle of radius 4 cm.
2π3
∴ Length of an arc =2π3. Was this answer helpful? Find, in terms of the π, the length of the arc that subtends an angle of 30∘ at the centre of a circle of radius 4 cm.
Consider the circle of radius ‘r’ below showing a sector containing an angle θ at the center.
The arc formed by the segments OA and OB is S and the angle it subtends at the centre is θ. The angle θ is given by the relationship:
Θ = S/r
Where r is the radius of the circle and is represented by the segments OA or OB. Hence, arc length
S = rΘ
Where Θ is typically in radians. In the given problem Θ = 30° and r = 4 cm
180° = π radians
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