Question

an oval track is made by erecting semicircles on each end of a 44 m by 88 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:

Identify track dimensions

The track consists of a central rectangle and two semicircles on each end.
The rectangle has a width (diameter of the semicircles) of \(d = 44\text{ m}\) and a length of \(L = 88\text{ m}\).
The radius of each semicircle is:

$$r = \frac{d}{2} = \frac{44}{2} = 22\text{ m}$$

Calculate track length

The length of the track (perimeter) is the sum of the two straight sides of the rectangle and the circumferences of the two semicircles.
The two semicircles combine to form one full circle with diameter \(d = 44\text{ m}\).
The perimeter \(P\) is:

$$P = 2L + \pi d$$

$$P = 2(88) + \pi(44)$$

$$P = 176 + 44\pi$$

Compute numerical length

Using the approximation \(\pi \approx 3.14159\):

$$P \approx 176 + 44(3.14159)$$

$$P \approx 176 + 138.23 = 314.23\text{ m}$$

Rounding to the nearest whole number gives \(314\text{ m}\).

Answer:

An oval track is made by erecting semicircles on each end of a 44 m by 88 m rectangle. Find the length of the track and the area enclosed by the track.

The length of the track is <blank>314</blank> <blank>\(\text{m}\)</blank>
(Round to the nearest whole number.)