The relationship of arcs is:
S '/ S = ((1/9) * pi * r) / (2 * pi * r)
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:
Clearing we have:
A = (A ') / (S' / S)
Substituting:
A = ((1/2) pi) / (1/18)
A = ((18/2) pi)
A = (9pi)
Answer:
The area of the circle is:
A = (9pi)