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 343 m. (round to the nearest whole number.) the area enclosed by the track is □ (round to the nearest whole number.)

Explanation:

Step1: Find the area of the rectangle

The rectangle has length \( l = 96 \) m and width \( w = 48 \) m. The area of a rectangle is \( A_{rectangle}=l\times w \).
\( A_{rectangle}=96\times48 = 4608 \) square meters.

Step2: Find the area of the two semicircles (which make a full circle)

The diameter of each semicircle is equal to the width of the rectangle, so the diameter \( d = 48 \) m, and the radius \( r=\frac{d}{2}=\frac{48}{2}=24 \) m. The area of a circle is \( A_{circle}=\pi r^{2} \).
\( A_{circle}=\pi\times(24)^{2}=\pi\times576\approx 3.1416\times576 = 1809.56 \) square meters.

Step3: Find the total area enclosed by the track

The total area is the sum of the area of the rectangle and the area of the circle (from the two semicircles).
\( A_{total}=A_{rectangle}+A_{circle}=4608 + 1809.56=6417.56\approx6418 \) square meters.

Answer:

The area enclosed by the track is \(\boxed{6418}\) square meters.