the diameter of a semi circle.

Question

On a quarter mile track, the straight parts are each 100 yards long. The curved ends are semicircles, also 110 yards long along the innermost rim. What is the diameter of the semicircle on each end?

Answer 1

1760 yards=1 mile, so ¼ mile=1760/4=440 yards.

The circumference of a circle is 2πr, where r is the radius (half the diameter). The curved part of a semicircle is πr.

The two straight parts of the track add up to 200 yards, so the semicircular ends take up 440-200=240 yards, which means that there are 120 yards for each semicircle. But the question says the curved parts of each semicircle are 110 yards long.

There is an inconsistency in this question, so let's assume the straight parts are each 110 yards long, not 100 yards, then we get 110 yards for each semicircular end.

So πr=110, r=110/π=35 yards approx., making the diameter about 70 yards.