What is the area of a sector with a central angle of 2pi/9 radians and a diameter of 20.6mm? Use 3.14 for Ali and round your answer to the nearest hundredth.

Accepted Solution

- The area of the circle is:


 A is the area of the circle.
 r is the radius of the circle.

 - To calculate the area of  the sector indicated in the problem, you must apply the following formula:


 As is the area of the sector.
 θ is the central angle (θ=2π/9)
 r is the radius.

 - First, you must find the radius:

 r=20.6 mm/2
 r=10.3 mm

 - Now, you can substitute the values into the formula As=(θ/2π)πr². Then, you have:


 - Finally, the area of the sector is:

 As= 37.01 mm²