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In the figure above, AC is the diameter of a circle with center O. If

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In the figure above, AC is the diameter of a circle with center O. If  [#permalink]

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New post 11 Apr 2018, 21:27
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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
Arc_Length.png [ 8.96 KiB | Viewed 719 times ]

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Re: In the figure above, AC is the diameter of a circle with center O. If  [#permalink]

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New post 12 Apr 2018, 00:31
The area = π*r^2 = 81π, >> radius = 9units.
Hence the required length of minor arc BC = [(180-110)/360] *[2*π*9] = 7π/2 = 3.5π (Option A)
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In the figure above, AC is the diameter of a circle with center O. If  [#permalink]

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New post 12 Apr 2018, 07:20
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Bunuel wrote:
Image
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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Re: In the figure above, AC is the diameter of a circle with center O. If  [#permalink]

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New post 16 Apr 2018, 16:18
Bunuel wrote:
Image
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


Since the area is 81π, the radius is 9, and the circumference is 18π.

Since a straight line has 180 degrees, we see that angle BOC measures 70 degrees. We calculate that angle BOC is 70/360 of the entire circle, so the length of minor arc BC is:

70/360 x 18π = 7/36 x 18π = 3.5π

Answer: A
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Re: In the figure above, AC is the diameter of a circle with center O. If &nbs [#permalink] 16 Apr 2018, 16:18
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