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Math Expert V
Joined: 02 Sep 2009
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If the perimeter of semicircle C is 4+4π, what is the radius of C?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 53% (01:24) correct 47% (01:10) wrong based on 128 sessions

HideShow timer Statistics If the perimeter of semicircle C is 4+4π, what is the radius of C?

A. 4+4/π
B. 4
C. (4+4π)/(2+π)
D. 2+2/(√π)
E. 2

Attachment: T6429.png [ 4.47 KiB | Viewed 2823 times ]

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GMAT 1: 750 Q49 V43 If the perimeter of semicircle C is 4+4π, what is the radius of C?  [#permalink]

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Bunuel wrote: If the perimeter of semicircle C is 4+4π, what is the radius of C?

A. 4+4/π
B. 4
C. (4+4π)/(2+π)
D. 2+2/(√π)
E. 2

Attachment:
T6429.png

Perimeter of a circle is $$2πr$$

Therefore perimeter of a semi-circle will be = half of perimeter of the circle, but notice that now the perimeter contains a straight line also (the diameter) which is 2r in length. This should also be added to calculate the perimeter of the semi-circle

$$\frac{1}{2} * 2πr + (2r)$$ =$$πr+2r$$

It is given that perimeter of semi-circle is $$4+4π$$

$$πr+2r= 4+4π$$

$$r(2+π)= 4+4π$$

$$r= \frac{4+4π}{2+π}$$

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Originally posted by LogicGuru1 on 15 Sep 2016, 04:38.
Last edited by LogicGuru1 on 19 Sep 2016, 09:34, edited 5 times in total.
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Joined: 26 Nov 2012
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Re: If the perimeter of semicircle C is 4+4π, what is the radius of C?  [#permalink]

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Bunuel wrote: If the perimeter of semicircle C is 4+4π, what is the radius of C?

A. 4+4/π
B. 4
C. (4+4π)/(2+π)
D. 2+2/(√π)
E. 2

Attachment:
T6429.png

Perimeter of semi-circle = r(π+2)

r(π+2) = 4+4π = > r = 4+4π/(π+2).

IMO option C.
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Re: If the perimeter of semicircle C is 4+4π, what is the radius of C?  [#permalink]

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4+4π = semi
r = 8+8π/2π
r=4+4π/π

A
Intern  B
Joined: 03 Sep 2016
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Re: If the perimeter of semicircle C is 4+4π, what is the radius of C?  [#permalink]

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It will be done as
Perimeter of semicircle will be arc length + straight length.. so Pi*r+2r ..

So,r(Pi+2)=4+4Pi
r = ( 4+4Pi)/ (2+Pi)
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Re: If the perimeter of semicircle C is 4+4π, what is the radius of C?  [#permalink]

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paidlukkha wrote:
4+4π = semi
r = 8+8π/2π
r=4+4π/π

A

You have missed something here. What is semi here?

Note : Semi Circle Perimeter = πr + 2r, 2r is the length of the diameter.
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Re: If the perimeter of semicircle C is 4+4π, what is the radius of C?  [#permalink]

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The answer would be c

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Re: If the perimeter of semicircle C is 4+4π, what is the radius of C?  [#permalink]

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_________________ Re: If the perimeter of semicircle C is 4+4π, what is the radius of C?   [#permalink] 05 Oct 2018, 16:13
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