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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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New post 27 Jun 2015, 05:42
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A
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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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New post 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 = \(3* \Pi\) / \(4* \Pi\) = \(3/4\)

Answer: option 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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New post 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)..
\(\frac{shaded area}{total}\)=\(\frac{R^2-r^2}{R^2}\)
\(\frac{(2r)^2-r^2}{(2r)^2}\)=\(\frac{3}{4}\)
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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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New post 27 Jun 2015, 18:15
Ans is D : 3/4

say radius of smaller circle=r2
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
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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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