Answer: r = 10 cm
Step-by-step explanation:
The formula for determining the area of a sector is expressed as
expressed as
Area of sector = θ/360 × πr²
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,
θ = 144°
Area of sector = 40π
Therefore,
40π = 144/360 × π × r²
40π × 360 = 144 × π × r²
14400π = 144πr²
Dividing through by π, it becomes
1440 = 144r²
r² = 14400/144
r² = 100
r = √100
r = 10 cm
