9514 1404 393
Answer:
398.12 m
Step-by-step explanation:
The perimeter fence consists of two half-circles (hence, a full circle) of radius 36.5 m, and two straight lengths of 84.39 m.
The circumference of a circle is given by the formula ...
C = 2πr
so the circular sections of fence have a total length of ...
C = 2π(36.5 m) = 73π m ≈ 229.34 m
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Adding the two straight lengths to this gives a total perimeter of ...
P = 2(84.39 m) +229.34 m = 398.12 m
The approximate length of the fence around the field shown is 398.12 m.
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Comment on significant figures
Since the length of the straight section is given to the nearest cm, we have elected to give the total length accurate to the nearest cm. If we assume that the radius is only good to 3 significant figures, then the circumference of the circle is good only to 3 significant figures (229 m). Thus, we must give our approximate value to the same precision, the nearest meter: 398 m.
