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# The area of circle O is 16pi, what is the length of an arc

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Current Student
Joined: 29 Jan 2005
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The area of circle O is 16pi, what is the length of an arc [#permalink]  02 Dec 2005, 05:33
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The area of circle O is 16pi, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?
Director
Joined: 13 Nov 2003
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if the area is 16pi then the lenght of the circle is 8pi and respectively the lenght of the arc required is 8pi/8 or pi
Director
Joined: 24 Oct 2005
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Re: PS Circle Arc Length [#permalink]  02 Dec 2005, 05:49
GMATT73 wrote:
The area of circle O is 16pi, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?

pi r^2 = 16 pi
r=4

n/360 * 2pi*r = length of arc

length of arc = 45/360 * 2*pi*4

= pi
Current Student
Joined: 29 Jan 2005
Posts: 5244
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Kudos [?]: 178 [0], given: 0

Yep, pi it is. Kaplan copied this one straight from the OG.
Manager
Joined: 20 Nov 2005
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Location: Indianapolis, IN
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Is the length of an arc formula something I should memorize?
Director
Joined: 24 Oct 2005
Posts: 660
Location: London
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Kudos [?]: 7 [0], given: 0

Is the length of an arc formula something I should memorize?

Would be nice to do,
Quite easy really.

length of arc = (n/360) * circumference of circle.
area of a sector = (n/360) * area of circle

n is the internal angle.
SVP
Joined: 05 Apr 2005
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GMATT73 wrote:
Yep, pi it is. Kaplan copied this one straight from the OG.

kaplan anf TPR are expert in copying questions from OG and claim that they are no 1 in test prep.

we should say the are no 1 in copying questions from OG.
SVP
Joined: 28 May 2005
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i got pi * r^2 = 16 pi

so r = 4

2 pi r = 8 pi

so 45 degree = 8 pi* 45/360 = pi
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Director
Joined: 04 Oct 2005
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Pi [#permalink]  02 Dec 2005, 14:22
Circumference of circle(360degree)=2pir
Circumference of circle(45degree)=2Pi*r/8=Pi*r/4

Area= 16Pi
Pi*(r^2)=16Pi
R=4

Circumference of arc= Pi*4/4=Pi
Senior Manager
Joined: 03 Nov 2005
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Location: Chicago, IL
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S(circle)=pi*r^2=16pi;r=4

Circumference=2pi*r=8pi

Length (arc)=fraction (Arc/360)*Circumference
l(arc)=45/360*8pi=1/8*8pi=pi
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