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

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Math Expert
Joined: 02 Sep 2009
Posts: 54410
A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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28 Mar 2019, 00:55
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Difficulty:

15% (low)

Question Stats:

94% (01:33) correct 6% (03:55) wrong based on 16 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 [ 10.71 KiB | Viewed 293 times ]

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Posts: 54410
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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28 Mar 2019, 00:58
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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Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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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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Manager
Joined: 13 Feb 2018
Posts: 206
GMAT 1: 640 Q48 V28
A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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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
L
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Joined: 25 Feb 2019
Posts: 198
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

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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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28 Mar 2019, 03:22
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

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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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