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