Answer:
Hence, the area of shaded region is:
![\dfrac{16\pi}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B16%5Cpi%7D%7B3%7D)
Step-by-step explanation:
We have to find the area of the smaller sectors that subtend an angle of 60° degree in the center.
Since the area of shaded portion is the area of circle excluding the area of smaller sectors.
We know that area of a sector is given as:
![Area=\dfrac{1}{2}r^2\phi](https://tex.z-dn.net/?f=Area%3D%5Cdfrac%7B1%7D%7B2%7Dr%5E2%5Cphi)
where φ is the angle in radians subtended to the center of the circle.
and r is the radius of the circle.
Now area of one sector with 60° angle is:
Firstly we will convert 60° to radians as:
![360\degree=2\pi\\\\60\degree=\dfrac{2\pi}{360}\times 60\\\\60\degree=\dfrac{\pi}{3}](https://tex.z-dn.net/?f=360%5Cdegree%3D2%5Cpi%5C%5C%5C%5C60%5Cdegree%3D%5Cdfrac%7B2%5Cpi%7D%7B360%7D%5Ctimes%2060%5C%5C%5C%5C60%5Cdegree%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D)
Hence, area of 1 sector is:
![Area=\dfrac{1}{2}\times 4^2\times \dfrac{\pi}{3}\\\\Area=\dfrac{8\pi}{3}](https://tex.z-dn.net/?f=Area%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%204%5E2%5Ctimes%20%5Cdfrac%7B%5Cpi%7D%7B3%7D%5C%5C%5C%5CArea%3D%5Cdfrac%7B8%5Cpi%7D%7B3%7D)
Now, area of 2 sector is:
![Area=2\times \dfrac{8\pi}{3}\\\\Area=\dfrac{16\pi}{3}](https://tex.z-dn.net/?f=Area%3D2%5Ctimes%20%5Cdfrac%7B8%5Cpi%7D%7B3%7D%5C%5C%5C%5CArea%3D%5Cdfrac%7B16%5Cpi%7D%7B3%7D)
Hence, the area of shaded region is:
![\dfrac{16\pi}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B16%5Cpi%7D%7B3%7D)