Verified Answer :

HomertheGenius

A central angle : π / 6 = 30 °
30 ° = 360 ° / 12
The area of the sector is 1/12 of the area of a circle.
Therefore area of the sector is:
A = 36 π / 12 = 3 π
Answer: A ) 3 π in²

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Area of a circle = 36π in²

As we know the formula for "Area of circle ":

\(Area=\pi r^2\\\\36\pi=\pi r^2\)

Now, we need to calculate the area of sector.

As we know the formula for "Area of sector":

\(Area\ of\ sector=\frac{\theta}{360\textdegree}\pi r^2\\\\Area\ of\ sector=\frac{30}{360}\times 36\pi \\\\Area\ of\ sector=\frac{1}{12}\times 36\pi\\\\Area\ of\ sector=3\pi\ in^2\)

Hence, Option 'A' is correct.

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