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A circle of radius 2 is inscribed in a semicircle, as shown. The area

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A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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New post 28 Mar 2019, 00:55
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A
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Difficulty:

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Question Stats:

92% (01:39) correct 8% (04:51) wrong based on 26 sessions

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A circle of radius 2 is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?

(A) 1/2

(B) \(\frac{\pi}{6}\)

(C) \(\frac{2}{\pi}\)

(D) 2/3

(E) \(\frac{3}{\pi}\)


Attachment:
b576665e4dd6ec10b3ec91bcda2f520bbd9d9846.png
b576665e4dd6ec10b3ec91bcda2f520bbd9d9846.png [ 10.71 KiB | Viewed 473 times ]

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Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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New post 28 Mar 2019, 00:58
Bunuel wrote:
Image
A circle of radius 2 is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?

(A) 1/2

(B) \(\frac{\pi}{6}\)

(C) \(\frac{2}{\pi}\)

(D) 2/3

(E) \(\frac{3}{\pi}\)


Attachment:
b576665e4dd6ec10b3ec91bcda2f520bbd9d9846.png


Check other Shaded Region Problems in our Special Questions Directory.
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Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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New post 28 Mar 2019, 01:29
Ans= Area of smaller circle/Area of semi circle
A= π2²/π4²/2
A=2*2²/4²=1/2

OA=A

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A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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New post 28 Mar 2019, 01:37
mohitranjan05 wrote:
Ans= Area of smaller circle/Area of semi circle
A= π2²/π4²/2
A=2*2²/4²=1/2

OA=A

Posted from my mobile device



The stem asks: \(\frac{area of semi - area of circle}{area of semi}\)

you just got lucky that area of semi - area of circle = area of circle
Otherwise, you could go wrong

Regards
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Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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New post 28 Mar 2019, 02:05
1
IMO A.

area of semicircle = (π 4^2)/2
= 16π/2=8π

area of inscribed circle = π 2^2 = 4π

aonthe shaded area = 8π-4π =4π

which is half of semicircle

so in fraction it is 1/2

IMO A

award kudoa if helpful

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Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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New post 28 Mar 2019, 03:22
area of semicircle ; 8 pi and of circle = 4pi
so ratio
4pi/8pi = 1/2
IMO A


Bunuel wrote:
Image
A circle of radius 2 is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?

(A) 1/2

(B) \(\frac{\pi}{6}\)

(C) \(\frac{2}{\pi}\)

(D) 2/3

(E) \(\frac{3}{\pi}\)


Attachment:
b576665e4dd6ec10b3ec91bcda2f520bbd9d9846.png
GMAT Club Bot
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area   [#permalink] 28 Mar 2019, 03:22
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A circle of radius 2 is inscribed in a semicircle, as shown. The area

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