EXAMPLE 3.7.6

Find the distance around the racetrack shown below.

A. 0.23 miles

B. 0.48 miles

C. 0.0067 miles

D. 0.35 miles

SOLUTION

In order to have enough information to solve this problem, we will have to make a reasonable assumption that was not stated in the problem, namely, that the figure consists of a rectangle with semicircles attached to its left and right sides:

Now we can express the total distance around the figure (in feet) as

300 + B + 100 + A, where A + B is equal to the circumference of a circle whose diameter is200 feet.

Thus, A + B = (pi)(200) = 628.319 feet (this has been rounded), so the total distance around the figure is roughly 628 feet + 300 feet + 300 feet = 1228 feet. Finally, we convert from feet to miles by dividing by 5280:

1228 feet = (1228 feet)/(5280 feet per mile) = .2326 miles (again, this has been rounded). The best choice is A.