Answer:
Hence, the area of shaded region is:
[tex]\dfrac{16\pi}{3}[/tex]
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:
[tex]Area=\dfrac{1}{2}r^2\phi[/tex]
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:
[tex]360\degree=2\pi\\\\60\degree=\dfrac{2\pi}{360}\times 60\\\\60\degree=\dfrac{\pi}{3}[/tex]
Hence, area of 1 sector is:
[tex]Area=\dfrac{1}{2}\times 4^2\times \dfrac{\pi}{3}\\\\Area=\dfrac{8\pi}{3}[/tex]
Now, area of 2 sector is:
[tex]Area=2\times \dfrac{8\pi}{3}\\\\Area=\dfrac{16\pi}{3}[/tex]
Hence, the area of shaded region is:
[tex]\dfrac{16\pi}{3}[/tex]
