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Difficult Math Question #53 - Geometry

This topic has 3 member replies
800guy Master | Next Rank: 500 Posts Default Avatar
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Difficult Math Question #53 - Geometry

Post Mon Nov 13, 2006 4:59 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to

    (A) 2/3
    (B) 3/4
    (C) 4/3
    (D) 3/2
    (E) 2

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    kulksnikhil Senior | Next Rank: 100 Posts Default Avatar
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    Post Tue Nov 14, 2006 10:30 pm
    800guy wrote:
    If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to

    (A) 2/3
    (B) 3/4
    (C) 4/3
    (D) 3/2
    (E) 2
    Answer is B 3/4

    Perimeter Of S = Perimeter of C
    4x = 2Pr (P=Pie =3.142)
    r = 2x/P

    Area S/Area C = x^2/Pr^2
    = x^2/P(2x/P)^2
    = x^2/P(4X^2/P^2)
    = 1/(4/P)
    = P/4

    P being 3.142 it is apprx equal to 3/4

    Bharadwaj Newbie | Next Rank: 10 Posts Default Avatar
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    Posted:
    6 messages
    Post Wed Nov 15, 2006 3:25 pm
    800guy wrote:
    If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to

    (A) 2/3
    (B) 3/4
    (C) 4/3
    (D) 3/2
    (E) 2
    B

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    Bharadwaj

    800guy Master | Next Rank: 500 Posts Default Avatar
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    Post Wed Nov 15, 2006 5:32 pm
    OA:

    and the answer would be B...here is the explanation...

    Let the side of the square be s..then the perimeter of the square is 4s
    Let the radius of the circle be r..then the perimeter of the circle is 2*pi*r

    it is given that both these quantities are equal..therefore

    4s=2*pi*r

    which is then s/r=pi/2

    Now the ratio of area of square to area of circle would be

    s^2/pi*r^2

    (1/pi)*(s/r)^2

    = (1/pi)*(pi/2)^2 from the above equality relation

    pi=22/7 or 3.14

    the value of the above expression is approximate =0.78 which is near to answer B

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