Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the area of the sector given r = 4 cm and Θ = pie/3
First, we need to find the length of the arc intercepted by the angle Θ. We know that the formula for the length of an arc is given by:
s = r * Θ
where s is the length of the arc, r is the radius, and Θ is the central angle in radians.
Given that r = 4 cm and Θ = π/3, we can plug in these values to find the length of the arc:
s = 4 * π/3
s = 4π/3
Next, we need to find the area of the sector enclosed by the angle Θ. The formula for the area of a sector is given by:
Area = (1/2) * r^2 * Θ
Plugging in the values we have, we get:
Area = (1/2) * 4^2 * π/3
Area = 8π/3
Therefore, the area of the sector enclosed by the angle Θ = π/3 with radius r = 4 cm is 8π/3 square centimeters.