Question

an oval track is made by erecting semicircles on each end of a 48 m by 96 m rectangle. find the length of the track and the area enclosed by the track. the length of the track is (round to the nearest whole number.)

Explanation:

Step1: Analyze the track's length components

The track length consists of two straight sides (from the rectangle) and two semicircles (which make a full circle). The length of the straight sides: each is 96 m, so two of them is \(2\times96\). The diameter of the semicircles is 48 m, so the radius \(r = \frac{48}{2}=24\) m. The circumference of a full circle is \(C = 2\pi r\) or \(\pi d\) (where \(d\) is diameter). Using \(\pi d\) here, \(d = 48\) m, so the circle's circumference is \(\pi\times48\).

Step2: Calculate the total length

Total length \(L=2\times96+\pi\times48\). Calculate \(2\times96 = 192\), \(\pi\times48\approx3.1416\times48\approx150.8\). Then \(L\approx192 + 150.8=342.8\), rounded to nearest whole number is 343.

Answer:

343