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Math Expert V
Joined: 02 Sep 2009
Posts: 58396
A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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Difficulty:   15% (low)

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

HideShow timer Statistics 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 [ 10.71 KiB | Viewed 473 times ]

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Math Expert V
Joined: 02 Sep 2009
Posts: 58396
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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Bunuel wrote: 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

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Manager  B
Joined: 31 Dec 2018
Posts: 114
Location: India
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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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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Senior Manager  G
Joined: 13 Feb 2018
Posts: 450
GMAT 1: 640 Q48 V28 A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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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
L
Senior Manager  G
Joined: 25 Feb 2019
Posts: 336
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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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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Joined: 18 Aug 2017
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Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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area of semicircle ; 8 pi and of circle = 4pi
so ratio
4pi/8pi = 1/2
IMO A

Bunuel wrote: 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 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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