Question

Find the area of the shaded sections. Click on the answer until the correct answer is showing.

Answer 1

If it the circle with the x in it and the x is shaded i got 16/3pi

Answer 2

Answer:

Hence, the area of shaded region is:

$\dfrac{16\pi}{3}$

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:

$Area=\dfrac{1}{2}r^2\phi$

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:

$360\degree=2\pi\\\\60\degree=\dfrac{2\pi}{360}\times 60\\\\60\degree=\dfrac{\pi}{3}$

Hence, area of 1 sector is:

$Area=\dfrac{1}{2}\times 4^2\times \dfrac{\pi}{3}\\\\Area=\dfrac{8\pi}{3}$

Now, area of 2 sector is:

$Area=2\times \dfrac{8\pi}{3}\\\\Area=\dfrac{16\pi}{3}$

Hence, the area of shaded region is:

$\dfrac{16\pi}{3}$