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555-605 (Medium)|   Geometry|      
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monirjewel
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The circle shown has center R. If arc UST has length 48\pi, what is th Updated on: 18 Aug 2015, 02:25
Originally posted by monirjewel on 09 Nov 2010, 00:54.
Last edited by Bunuel on 18 Aug 2015, 02:25, edited 1 time in total.
Renamed the topic and edited the question.
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C
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Difficulty:

25% (medium)

Question Stats:

76% (01:24) correct 24% (02:02) wrong based on 147 sessions

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The circle shown has center R. If arc UST has length \(48\pi\), what is the radius of the circle?

A. 18
B. 24
C. 32
D. 48
E. 64
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C

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Bunuel
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The circle shown has center R. If arc UST has length 48\pi, what is th 09 Nov 2010, 01:00
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monirjewel
How to solve this problem? Thanks in advance
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The circle shown has center R. If arc UST has length 48p, what is the radius of the circle?
A. 18
B. 24
C. 32
D. 48
E. 64

Circumference of a circle (360 degrees) equals to \(2\pi{r}\);

Arc UST is 360-90=270 degrees, so the length of this arc equals to \(\frac{270}{360}*2\pi{r}=48\pi\) --> \(r=32\).

Answer: C.

For more on this issues check Circles chapter of Math Book: math-circles-87957.html

Hope it helps.
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The circle shown has center R. If arc UST has length 48\pi, what is th 09 Nov 2010, 03:47
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Remember the formula- Arc Length= (Arc angle*circumference)/360
after calculations- radius=32

Answer:- C
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The circle shown has center R. If arc UST has length 48\pi, what is th 09 Nov 2010, 08:22
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Simple I messed it up in the calculation ....
Answer should be C

(3/4)*2r = 48 => r = 16*2 = 32
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The circle shown has center R. If arc UST has length 48\pi, what is th 09 Nov 2010, 18:44
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The concept here is the relation between the length of the arc and the circumference
Formula is: Arc length=(arc degree/360)(circumference). In this case it translates to (270/360)(2PieR). Set this = to 48Pie and solve for Pie.
NB: Know the relationship between the Arc length and the Circumference/Area of the circle.
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The circle shown has center R. If arc UST has length 48\pi, what is th 09 Apr 2022, 03:06
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