Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the arc length given the circle area A = 16π cm2 and Θ = π 3 .
Answer: The length of the arc is: L=4π/3 cm
Length of arc: L=?
L=r Θ
Central angle: Θ=π/3
Radius: r=?
Area of the circle: A=16π cm^2
A=π r^2
Replacing A=16π cm2 in the equation above:
16π cm^2=π r^2
Solving for r: Dividing both sides of the formula by π:
(16π cm^2)/π=(π r^2)/π
16 cm^2=r^2
Square root both sides of the formula:
sqrt( 16 cm^2)=sqrt(r^2)
4 cm=r
r=4 cm
L=r Θ
L=(4 cm)π/3
L=4π/3 cm