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Math Help - geometry length

  1. #1
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    geometry length

    see attatched pic
    the diagram shows a running track with the 'straights' 90m ling and with semicircular end sections.if the inside distance is 400m and the track is 8m wide, how much further is it to run around the outside of the track?
    Attached Thumbnails Attached Thumbnails geometry length-math2.jpg  
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  2. #2
    MHF Contributor
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    Quote Originally Posted by mrmann View Post
    see attatched pic
    the diagram shows a running track with the 'straights' 90m ling and with semicircular end sections.if the inside distance is 400m and the track is 8m wide, how much further is it to run around the outside of the track?
    Where are the "straights" in the diagram? The diagram as posted shows two "concentric" ellipses only.

    Anyway, I understand what you mean because we constructed a few of those ovals before.

    The inside track:
    (Assumed to be the innermost of the oval for this exercise)
    Perimmeter, P1 = 400m
    P1 = (two semicircles) +2(90) = 400
    two semicircles = 400 -180 = 220
    one circle = 220 m in circumference
    radius, r = 220 / 2pi = 110/pi meters.

    The outdside track:
    (assumed also to be the outermost of the oval for this exercise.)
    radius, R = r +8 = (110/pi0 +8
    So,
    Perimeter, P2 = (two semicircles) +2(90)
    P2 = one circle +180
    P2 = 2pi[(110/pi) +8] +180
    P2 = 220 +16pi +180
    P2 = 400 +16pi meters

    So, P2 -P1 = (400 +16pi) -400 = 16pi
    Meaning, it takes 16pi meters more to run around the outside track.
    In decimals, that is 50.27 meters more.
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