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The circumference of a circle is 144 cm. If an arc's length

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sudhagar
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The circumference of a circle is 144 cm. If an arc's length [#permalink] New post   18 Oct 2005, 09:35
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The circumference of a circle is 144 cm. If an arc's length
is 24 cm, how many degrees are there in the arc?

A. 60
B. 24
C. 16 2/3
D. 50
E. 35



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Re: The circumference of a circle is 144 cm. If an arc's length [#permalink] New post   18 Oct 2005, 09:38
Circumference = 360 degrees arc = 144cm
24cm = 24/144 * 360 = 60 degrees
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Re: The circumference of a circle is 144 cm. If an arc's length [#permalink] New post   18 Oct 2005, 09:40
A. 60

arc to circumference proportion:
24/144 or 1/6
angle this arc makes should also be in the same proportion. so
angle = 360 / 6 = 60
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Re: The circumference of a circle is 144 cm. If an arc's length [#permalink] New post   18 Oct 2005, 13:43
OA is A.

Here goes the detailed explanation:
This problem can be solved with the formula

Arc Length = Circumference * ((Arc Measure)/360)

Solving for Arc Measure,

24 cm = 144 cm * ((Arc Measure)/360)
24 cm/144 cm = ((Arc Measure)/360)
24 cm * 360 = (Arc Measure) * 144 cm
8640 cm = (Arc Measure) * 144 cm
8640 cm/144 cm = Arc Measure
Arc Measure = 60
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Re: The circumference of a circle is 144 cm. If an arc's length [#permalink] New post   19 Oct 2005, 02:37
A.

Length of the arc = (n/360)(Circumference)
24 = (n/360)(144), solving for n we get n = 60



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Re: The circumference of a circle is 144 cm. If an arc's length [#permalink]
19 Oct 2005, 02:37
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