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The figure above displays two semicircles, one with diameter AB and on

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The figure above displays two semicircles, one with diameter AB and on  [#permalink]

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New post 11 Jan 2019, 01:30
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Difficulty:

  25% (medium)

Question Stats:

73% (01:40) correct 27% (01:53) wrong based on 34 sessions

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The figure above displays two semicircles, one with diameter AB and one with diameter AC. If AB has a length of 4 and AC has a length of 6, what fraction of the larger semicircle does the shaded region represent?

A. 1/3

B. 4/9

C. 1/2

D. 5/9

E. 2/3

Attachment:
2019-01-11_1228.png
2019-01-11_1228.png [ 15.2 KiB | Viewed 474 times ]

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The figure above displays two semicircles, one with diameter AB and on  [#permalink]

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New post Updated on: 11 Jan 2019, 04:42
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Bunuel wrote:
Image
The figure above displays two semicircles, one with diameter AB and one with diameter AC. If AB has a length of 4 and AC has a length of 6, what fraction of the larger semicircle does the shaded region represent?

A. 1/3

B. 4/9

C. 1/2

D. 5/9

E. 2/3

Attachment:
2019-01-11_1228.png


small circle area = pi * 4 and large circle area = pi * 9
shaded region = (9-4) * pi
fraction of the larger semicircle does the shaded region represent
5 * pi/ pi * 9 = 5/9 IMO d
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Originally posted by Archit3110 on 11 Jan 2019, 03:27.
Last edited by Archit3110 on 11 Jan 2019, 04:42, edited 1 time in total.
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Re: The figure above displays two semicircles, one with diameter AB and on  [#permalink]

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New post 11 Jan 2019, 04:35
Bunuel wrote:
Image
The figure above displays two semicircles, one with diameter AB and one with diameter AC. If AB has a length of 4 and AC has a length of 6, what fraction of the larger semicircle does the shaded region represent?

A. 1/3

B. 4/9

C. 1/2

D. 5/9

E. 2/3

Attachment:
2019-01-11_1228.png


Area of semi-circle pi/2 * r^2

diameter AB = 4 and diameter AC = 6
r(AB) = 2 and r(AC) = 3

Shaded region = pi/2 * [ r(AC)^2 - r(AB)^2)] = pi/2 *5 -------(1)
Area of larger semicircle = pi/2 * 9-------(2)

what fraction of the larger semicircle does the shaded region represent = (1)/(2)
=> 5/9

Answer D
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Re: The figure above displays two semicircles, one with diameter AB and on  [#permalink]

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New post 11 Jan 2019, 12:12
Area of larger semicircle= (pi/2)* (AC/2)^2=0.5pi*3^2= 4.5pi
Area of smaller semicircle= (pi/2)* (AB/2)^2=0.5pi*2^2= 2pi

Area of shaded portion= Area of larger semicircle-area of smaller semicircle= 4.5pi-2pi=2.5pi

Thus, ratio = 2.5pi/4.5pi=5/9
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Re: The figure above displays two semicircles, one with diameter AB and on   [#permalink] 11 Jan 2019, 12:12
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The figure above displays two semicircles, one with diameter AB and on

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