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area of circular region

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ifthyder Really wants to Beat The GMAT! Default Avatar
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area of circular region Post Wed Oct 15, 2008 8:44 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    please explain each bit of details?
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    parallel_chase GMAT Titan Default Avatar
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    Post Wed Oct 15, 2008 8:54 am
    Since 30,40 are the points on the circle, the distance from the origin to the point on the circle will be the radius.

    r^2 = 30^2 + 40^2

    r = sqrt 2500

    r = 50

    area = pi r^2 = 50^2 pi = 2500 pi.

    Hence D.

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    Post Wed Oct 15, 2008 9:50 am
    parallel_chase wrote:
    Since 30,40 are the points on the circle, the distance from the origin to the point on the circle will be the radius.

    r^2 = 30^2 + 40^2

    r = sqrt 2500

    r = 50

    area = pi r^2 = 50^2 pi = 2500 pi.

    Hence D.
    Good solution using the Pythagorean formula.

    We can shave some time off if we quickly recognize a 3x:4x:5x triangle in the mix. 3/4/5 is the most commonly tested Pythagorean triplet and almost always shows up in some form on test day.

    As soon as you see that you have a 30/40/x right angle triangle, 50 should come to mind as the radius. Then calculate the area as above.

    Other important triplets to know:

    5x:12x:13x
    x:x:xroot2 (right isosceles triangle)
    x:xroot3:2x (30/60/90 triangle)

    and less tested, but still comes up:

    7x:24x:25x

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    Last edited by Stuart Kovinsky on Thu Oct 16, 2008 12:59 pm; edited 1 time in total

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    rohangupta83 GMAT Destroyer! Default Avatar
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    Post Thu Oct 16, 2008 2:01 am
    (D)

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