Exercises
28. The athletis track on the right consists of two straight parts that are both 100 metres long, and two curved parts. The sides of the curved parts are semicircles. The inside semicircles have a radius of 31.83 metres. The athletics track is 10 metres wide.
A. Calculate te length of one lap of the inside lane of the track.
circumference = ∏ x radius x 2
c = ∏ x 31.83 x 2
c = 199.99 meter
c = 199.99 + 100 + 100
c ≈ 400 metres
B. The track is to be made faster by adding a layer of a special material. How many m2 of this material is needed?
Area of the big circle = ∏ x r x r
A = ∏ x 41.83 x 41.83
A = 5496.998
Area of the small circle = ∏ x r x r
A = ∏ x 31.83 x 31.83
A = 3182.901
5496.998 - 3182.901 = 2314.097 m2
2314.097 + 2000 = 4314 metre
So 4314 metre2 of special material is needed.