Find the area of a sector with central angle 4𝜋/9 rad in a circle of radius 20 m. (Round your answer to one decimal places.)
The formula to find the area of a sector is given by:
Area of sector = (𝜋r²θ)/2
where r is the radius of the circle and θ is the central angle in radians.
Substituting the given values into the formula:
Area of sector = (𝜋(20)²(4𝜋/9))/2
Area of sector = (400𝜋²/9)/2
Area of sector = 200𝜋²/9
Approximating 𝜋 as 3.14 and rounding to one decimal place, the area of the sector is:
Area of sector ≈ 221.39 square meters