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Circles

by harsh.champ » Sun Feb 07, 2010 7:43 am
The diameter of the smaller circle is equal to the side of the square and the diagonal of the square is equal to the diameter of the bigger circle. If the circles are concentric, then their areas are in the ratio:-

(A)1:2
(B)2:3
(C)1:sqrt(2)
(D)1:4
(E)None of these
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by shashank.ism » Sun Feb 07, 2010 7:52 am
harsh.champ wrote:The diameter of the smaller circle is equal to the side of the square and the diagonal of the square is equal to the diameter of the bigger circle. If the circles are concentric, then their areas are in the ratio:-

(A)1:2
(B)2:3
(C)1:sqrt(2)
(D)1:4
(E)None of these


Let r be the radius of smaller circle = r.
so edge length of square = 2r
length of diagonal of square = sqrt.((2r)^2+(2r)^2) = 2r.2^0.5
radius of bigger circle = 2r.2^0.5/2 =r.2^0.5

so ratio of area of circle = pie . r^2/ pie. (r.2^0.5)^2 = 1/2.

The Ans is [spoiler](A)[/spoiler]
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by ajith » Sun Feb 07, 2010 8:06 am
harsh.champ wrote:The diameter of the smaller circle is equal to the side of the square and the diagonal of the square is equal to the diameter of the bigger circle. If the circles are concentric, then their areas are in the ratio:-

(A)1:2
(B)2:3
(C)1:sqrt(2)
(D)1:4
(E)None of these
say Diameter of the small circle = a
diagonal of the of the square = sqrt(2)*a
Diameter of the bigger circle = sqrt(2)*a

The ratio of area of smaller and bigger circle = pi*a^2/pi*(sqrt(2)*a)^2
= 1/(sqrt(2))^2 = 1/2
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