Circles

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

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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Source: Beat The GMAT — Problem Solving | Sun Feb 07, 2010 7:43 am

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

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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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

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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