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

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Senior Manager
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The circumference of a circle is 144 cm. If an arc's length  [#permalink] New post 18 Oct 2005, 08:35
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A
B
C
D
E

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0% (00:00) correct 0% (00:00) wrong based on 1 sessions
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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 [#permalink] New post 18 Oct 2005, 08:38
Circumference = 360 degrees arc = 144cm
24cm = 24/144 * 360 = 60 degrees
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 [#permalink] New post 18 Oct 2005, 08:40
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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 [#permalink] New post 18 Oct 2005, 12:43
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: PS: Circumference + Arc [#permalink] New post 19 Oct 2005, 01:37
A.

Length of the arc = (n/360)(Circumference)
24 = (n/360)(144), solving for n we get n = 60
Re: PS: Circumference + Arc   [#permalink] 19 Oct 2005, 01:37
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