The relationship of arcs is:
S '/ S = ((1/9) * pi * 3) / (2 * pi * 3)
Rewriting we have:
S '/ S = ((1/9)) / (2)
S '/ S = 1/18
Therefore, the area of the shaded region is:
A '= (S' / S) * A
Where A: area of the complete circle:
A '= (1/18) * pi * r ^ 2
A '= (1/18) * pi * (3) ^ 2
A '= (1/18) * pi * 9
A '= (1/2) * pi
Answer:
The area of the shaded region is:
A '= (1/2) * pi