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Re: Circle A has area a Semicircle B has area a/2 [#permalink]
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saifulislampharmadu wrote:
Here A and 2*B circle has same area.hence same perimeter
Perimeter of 2*B circle=twice the perimeter of B=perimeter of A

So ans is (C)

Posted from my mobile device Image


Circle A and B have the same area i.e. same radius.
However the option B is stated as = \(2 \times(\pi r +2r)\). Twice the perimeter of semicirle B is not Equal to perimeter of circle B since there is an additional term of the diameter in the perimeter.
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Re: Circle A has area a Semicircle B has area a/2 [#permalink]
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Here is a picture that illustrates that perimeter of two semi-circles is equal to one circle plus two diameters.
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two semicircles.jpg
two semicircles.jpg [ 23.08 KiB | Viewed 8657 times ]

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Re: Circle A has area a Semicircle B has area a/2 [#permalink]
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sandy wrote:
Circle A has area \(a\)
Semicircle B has area \(a/2\)

Quantity A
Quantity B
The circumference of Circle A
Twice the perimeter of semicircle B


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


GIVEN: Semicircle B has area \(a/2\)
GIVEN: Circle A has area \(a\)
Image


Since a semicircle is HALF of a circle, we can conclude that, if we combine TWO of semicircle B, the combined area will be \(a\)
Image
In other words, the red and blue circles above must have the same area.

If the red and blue circles have the same area, their radii must also be equal.
So let's let r = the radius of the red circle
This means r = the radius of the blue semicircle
Image

At this point we can compare the two quantities.

QUANTITY A: The circumference of Circle A = 2πr

QUANTITY B: TWICE the perimeter of semicircle B
The perimeter of ONE semicircle B = (length of curved portion) + (length of straight diameter)
= (0.5)(2πr) + (2r)
= πr + 2r

So, TWICE the perimeter of semicircle B = 2(πr + 2r)
= 2πr + 4r

Since 2πr + 4r > 2πr, the correct answer is B.

Cheers,
Brent
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Re: Circle A has area a Semicircle B has area a/2 [#permalink]
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