Answer: the radius of the circle is 22.5 cm
Step-by-step explanation:
The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Length of arc = 20π cm
θ = 160 degrees
Therefore,
20π = 160/360 × 2 × π × r
20π = 160/360 × 2 × π × r
Dividing both sides of the equation by π, it becomes
20 = 160/360 × 2r
20 × 360 = 160 × 2r = 320r
320r = 7200
r = 7200/320
r = 22.5 cm
