Bunuel wrote:

In the figure above, AC is the diameter of a circle with center O. If the area of the circle is 81π, what is the length of minor arc BC?

A. 3.5π

B. 6π

C. 7π

D. 8.5π

E. 9π

Attachment:

Arc_Length.png

The length of minor arc BC is a fraction of the circumference.

That fraction is determined by the central angle of sector BOC.

That central angle, also called BOC, lies on a straight line with another angle of 110°

Angle BOC = 70°

Straight line = 180°

(180° - 110°) = 70°

Sector BOC = what fraction of the circle:

\(\frac{Part}{Whole}=\frac{SectorAngle}{360°}=\frac{70}{360}=\frac{7}{36}\) of circle

Sector BOC =

\(\frac{7}{36}\) of the circle

Circumference of circle?

Find the radius from the area, given

\(A = \pi r^2 = 81\pi\)

\(r^2 = 81\)

\(r = 9\)So circumference =

\(2\pi r=18\pi\)Arc BC is

\(\frac{7}{36}\) of circumference

\((\frac{7}{36}*18\pi)=\frac{7}{2}\pi=3.5\pi\)Answer A

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