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

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

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New post 15 Sep 2016, 03:10
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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

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T6429.png
T6429.png [ 4.47 KiB | Viewed 2136 times ]

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

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New post Updated on: 19 Sep 2016, 08:34
Bunuel wrote:
Image
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


Answer is C

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 \(4+4π\)

\(πr+2r= 4+4π\)

\(r(2+π)= 4+4π\)


\(r= \frac{4+4π}{2+π}\)

ANSWER IS C
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Originally posted by LogicGuru1 on 15 Sep 2016, 03:38.
Last edited by LogicGuru1 on 19 Sep 2016, 08:34, edited 5 times in total.
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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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New post 15 Sep 2016, 04:08
Bunuel wrote:
Image
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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New post 15 Sep 2016, 04:31
4+4π = semi
r = 8+8π/2π
r=4+4π/π

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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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New post 15 Sep 2016, 20:05
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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New post 17 Sep 2016, 05:04
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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New post 17 Sep 2016, 21:25
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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