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11 Apr 2018, 21:27
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A
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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 [ 8.96 KiB | Viewed 6354 times ]
12 Apr 2018, 07:20
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Bunuel
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
