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If the diameter of the given circle is 36, what is the length of the a

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If the diameter of the given circle is 36, what is the length of the a  [#permalink]

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New post 13 Oct 2018, 09:44
5
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A
B
C
D
E

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  45% (medium)

Question Stats:

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If the diameter of the given circle is 36, what is the length of the arc ABC?
A) 8pi
B) 22pi
C) 28pi
D) 32pi
E) Cannot be determined

Weekly Quant Quiz #4 Ques 10


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Re: If the diameter of the given circle is 36, what is the length of the a  [#permalink]

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New post 13 Oct 2018, 20:31

Official Solution


In DS Questions and PS Question with an option can not be determined should give you a flag to think whether it is possible to find the answer or not?
if you try to visualize the question, we get that we are given a circle with a fixed diameter, and angle between the chord.
What is asked ? = Length of arc ABC
by simply drawing the figure , it will be realized that the point A is not fixed and this can lead to different length of arc ABC.
Hence it can not be determined.
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Re: If the diameter of the given circle is 36, what is the length of the a  [#permalink]

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New post 13 Oct 2018, 09:59
I think the answer to this question should be the option (E). Please find my solution attached.

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Re: If the diameter of the given circle is 36, what is the length of the a  [#permalink]

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New post 13 Oct 2018, 09:59
Answer is A 8 pi. Screenshot attached
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Re: If the diameter of the given circle is 36, what is the length of the a  [#permalink]

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New post 13 Oct 2018, 10:03
C. 28 pi

Approach -
1. Find the length of an arch of B to C and
2. Find the length of the entire arc of the circle
3. Subtract it from the total length of the circle arc

1. Find the length of an arc B to C
Length of an arc X / 360 * 2 pi r
i.e. 40/360 * 2 * pi * 18 = 4 pi

2. Total 320 / 360 * 2 * pi * 18 = 32 pi

3. 32 pi - 4 pi = 28 pi
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Re: If the diameter of the given circle is 36, what is the length of the a  [#permalink]

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New post 13 Oct 2018, 10:21
say , center of the circle O. angle BAC= 40 thus angle BOC=80

arc ABC = arc BC + 1/2 arec BAC = (80/360)*2*18pi + 1/2*{(360-80)/360}*18pi = 8pi+14pi=22pi .......Ans B
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Re: If the diameter of the given circle is 36, what is the length of the a   [#permalink] 13 Oct 2018, 10:21
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