I need help on a math homework!! Here's the problem: What is the radius of the semicircle that forms the curve of a 400 meter track race if each straightaway is 116m long? (round to nearest tenths place)
2007-01-17 18:40:19 · 7 answers · asked by blackrose 3 in Science & Mathematics ➔ Mathematics
Ok. So the whole race track is 400 meters. Now, each straightaway is 116m.
There are 2, so double that. 116 x 2 = 232.
To get the remaining track 400- 232= 168.
Now, since there are two semicircles on either side, we divide this by 2. 168/2=84 m.
Now, this value, 84m, give us the CIRCUMFERENCE of each semicircle.
CIRCUMFERENCE, denoted "C", of a WHOLE circle = 2(pi)r, where r= radius and pi=3.141592654....(it's on your calculator)
So, the circumference of the semicircle is 2(pi)r/2= (pi)r
Now, we know the circumference, 84m and the value of (pi). So, to find r, divide 84m by (pi)
r=26.7 m
2007-01-17 18:52:37 · answer #1 · answered by Ace 4 · 0⤊ 0⤋
the track is formed of 2 straight ways and 2 semicircle
Perimeter of track is 400
if we take away the 2 straight ways
we'll have the perimeter of the 2 half circles
so Pc=400 - 2*116 = 168m so each semi circle has a perimeter of 84m and
Perimeter of 1/2 circle= Pi * R = 84 so R = 26.74 m
2007-01-17 18:59:58 · answer #2 · answered by Anonymous · 0⤊ 0⤋
It's set up like this:
____
(____)
If you have the lengths of the ____s, then what you're left with is the circle, right? You have the ( ) remaining. So you subtract 2(116) from 400, and you're left with 168, which is the circumference of the circle. Divide the circumference by pi to get the diameter, and divide that by 2. Total is 26.8 (if you estimate pi to be 3.14).
2007-01-17 18:47:48 · answer #3 · answered by supensa 6 · 2⤊ 0⤋
the 2 curves are 400-2*116=168m each 1 is 168/2=84m
the circunference of a semecircle is Î r
84=Î r
r=84/Î =26.7m
2007-01-17 18:53:09 · answer #4 · answered by yupchagee 7 · 0⤊ 0⤋
116*2 = 232m (length of straightway)
total lenth (400m) - straightway (232m) = length of 2 semicircle arcs (168m)
length of 1 arc = 168m/2 = 84m
From this, you already know that the answer will be < 84m/2 = 48m. C = 84*2 = 168m
C(ircumference) = 2*pi*r
solve for r:
168 = 2*pi*r
r = 168/(2*pi) ~ 26.8
2007-01-17 18:51:12 · answer #5 · answered by vaca loca 3 · 0⤊ 0⤋
do you know how late it is? you should have asked when people in your house were awake! but honestly hun, i dont know, go look up the definitions and get a protracter, itll probobly be easier
2007-01-17 18:44:56 · answer #6 · answered by PrinceKattJohnnyDepp 2 · 0⤊ 2⤋
26.8 m
2007-01-17 18:44:54 · answer #7 · answered by camus140 2 · 0⤊ 0⤋