Answer:
r = 5 units
Step-by-step explanation:
Given:
Angle subtended at the centre (∅) in radians = 2π/3
Arc length (S) = 10π/3
radius (r) = ?
Required:
Radius (r)
Solution:
Formula for arc length given the central angle in radians is:
S = r∅
Make e the subject of the formula by dividing both sides by ∅
S/∅ = r∅/∅
r = S/∅
Plug in the values
r = (10π/3) / (2π/3)
Change the operation sign to multiplication and turn the fraction by your right upside down
r = 10π/3 × 3/2π
r = (10π × 3)/(3 × 2π)
Cross out terms that can divided each other
r = 5
