Question

pretest: circles
the transportation department has to put a railing along the outer curve of this road. the road is 20 feet wide. what is the length of the outer curve to the nearest foot? use the value π = 3.14.
(image of a curved road with inner radius 50 feet, width 20 feet, and central angle 70°)
a. 68 feet
b. 74 feet
c. 86 feet
d. 92 feet
e. 102 feet

Explanation:

Step1: Find outer curve radius

The inner radius is 50 ft, road width is 20 ft.
$R = 50 + 20 = 70$ feet

Step2: Recall arc length formula

Arc length $L = \frac{\theta}{360^\circ} \times 2\pi R$, where $\theta=70^\circ$, $\pi=3.14$

Step3: Substitute values and calculate

$L = \frac{70^\circ}{360^\circ} \times 2 \times 3.14 \times 70$
First calculate $2 \times 3.14 \times 70 = 439.6$
Then calculate $\frac{70}{360} \times 439.6 \approx 0.1944 \times 439.6 \approx 85.4$

Step4: Round to nearest foot

$85.4 \approx 86$ feet

Answer:

C. 86 feet