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# Which is greater: Length of arc ABC or 6?

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Senior Manager
Joined: 20 May 2014
Posts: 282
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Kudos [?]: 50 [0], given: 220

Which is greater: Length of arc ABC or 6? [#permalink]  29 Oct 2017, 01:31
00:00

Question Stats:

100% (00:22) correct 0% (00:00) wrong based on 9 sessions

 Quantity A Quantity B Length of arc ABC 6

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Kudos for correct solution.

[Reveal] Spoiler:
Attachment:

Geometry - QC - circle arc length_q.PNG [ 6.69 KiB | Viewed 941 times ]
[Reveal] Spoiler: OA
Director
Joined: 03 Sep 2017
Posts: 521
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Kudos [?]: 344 [1] , given: 66

Re: Which is greater: Length of arc ABC or 6? [#permalink]  30 Oct 2017, 07:06
1
KUDOS
The length of an arc is proportional to the correspondent angle at the center. Thus, given that the angle here is 60°, it is 1/6 of the entire angle of 360°. In the same way, the arc ABC is 1/6 of the full circumference that is $$2r\pi = 12\pi$$. Then, the arc is $$\frac{1}{6}12\pi = 3\pi > 6$$ long. Thus, quantity A is greater.

Re: Which is greater: Length of arc ABC or 6?   [#permalink] 30 Oct 2017, 07:06
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