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# If the center of a circle lies on a smaller circle, as shown above, wh

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If the center of a circle lies on a smaller circle, as shown above, wh  [#permalink]

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27 Jun 2015, 05:42
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5% (low)

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96% (01:12) correct 4% (02:02) wrong based on 44 sessions

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T6099.png [ 8.17 KiB | Viewed 1231 times ]

If the center of a circle lies on a smaller circle, as shown above, what portion of the area of the larger circle is shaded?

A. 5/8
B. 2/3
C. 11/16
D. 3/4
D. 7/9
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Re: If the center of a circle lies on a smaller circle, as shown above, wh  [#permalink]

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27 Jun 2015, 07:10
reto wrote:
Attachment:
T6099.png

If the center of a circle lies on a smaller circle, as shown above, what portion of the area of the larger circle is shaded?

A. 5/8
B. 2/3
C. 11/16
D. 3/4
D. 7/9

Let, Radius of Bigger Circle, R = 2
Radius of Smaller Circle, r = 2/2 = 1

Shaded Area =$$\Pi (R^2 - r^2)$$ = $$\Pi (2^2 - 1^2)$$ = $$3*\Pi$$

Area of Bigger Circle = $$\Pi (R^2)$$ = $$\Pi (2^2)$$ =$$4* \Pi$$

Required Fraction = Shaded Area / Area of Bigger Circle = $$3* \Pi$$ / $$4* \Pi$$ = $$3/4$$

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Re: If the center of a circle lies on a smaller circle, as shown above, wh  [#permalink]

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27 Jun 2015, 07:21
reto wrote:
Attachment:
T6099.png

If the center of a circle lies on a smaller circle, as shown above, what portion of the area of the larger circle is shaded?

A. 5/8
B. 2/3
C. 11/16
D. 3/4
D. 7/9

Ratios of area will be in the ratio of radius..
radius of bigger circle(R) is 2*smaller one (r)..
$$\frac{shaded area}{total}$$=$$\frac{R^2-r^2}{R^2}$$
$$\frac{(2r)^2-r^2}{(2r)^2}$$=$$\frac{3}{4}$$
D
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Re: If the center of a circle lies on a smaller circle, as shown above, wh  [#permalink]

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27 Jun 2015, 18:15
Ans is D : 3/4

radius of bigger circle = r1

r1=2r2

portion of the area of shared region: pi r2^2

pi (2r2)^2-pi r2^2=3/4 pi r1^2

what portion of the area of the larger circle is shaded?
= 3/4 pi r1^2/pi r1^2 =3/4

Ans D
Re: If the center of a circle lies on a smaller circle, as shown above, wh   [#permalink] 27 Jun 2015, 18:15
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