The correct approximate distance a car will travel between Cole Street and Maple Street along the shorter route of the roundabout is [tex]\boxed{107.2 \text{ feet}}[/tex].
To find the approximate distance a car will travel between Cole Street and Maple Street along the roundabout, we need to consider the geometry of the roundabout. Since the roundabout is a circle with a diameter of 130 feet, its radius (r) is half of the diameter, which is [tex]\( r = \frac{130}{2} = 65 \) feet[/tex].
The shorter route between Cole Street and Maple Street will be along the arc that subtends the angle at the center of the roundabout between the two streets. To find this arc length (s), we use the formula for the arc length of a circle, which is [tex]\( s = r \theta \)[/tex], where [tex]\( \theta \)[/tex] is the central angle in radians.
Since we are looking for the shorter route, we are interested in the angle that is less than 180 degrees. The roundabout is divided into four equal parts by the four streets, so the central angle between any two adjacent streets is [tex]\( \frac{360^\circ}{4} = 90^\circ \)[/tex].
To convert degrees to radians, we use the conversion factor [tex]\( \frac{\pi \text{ radians}}{180^\circ} \)[/tex]. Therefore, the angle in radians is [tex]\( \theta = 90^\circ \times \frac{\pi \text{ radians}}{180^\circ} = \frac{\pi}{2} \)[/tex] radians.
Now we can calculate the arc length:
[tex]\[ s = r \theta = 65 \text{ feet} \times \frac{\pi}{2} \][/tex]
Using the approximation [tex]\( \pi \approx 3.14159 \)[/tex], we get:
[tex]\[ s \approx 65 \text{ feet} \times \frac{3.14159}{2} \approx 107.2 \text{ feet} \][/tex]
Thus, the approximate distance a car will travel between Cole Street and Maple Street along the shorter route of the roundabout is 107.2 feet.
