Question

the radius of the circle shown below is 7 inches. what is the approximate length of \\(\overarc{ab}\\)? \
\
a. 16.5 in \
b. 57.7 in \
c. 8.2 in \
d. 44.0 in

Explanation:

Step1: Recall arc length formula

The formula for arc length is $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle, $r$ is the radius.

Step2: Substitute given values

$\theta = 135^\circ$, $r = 7$ inches.
$L = \frac{135^\circ}{360^\circ} \times 2\pi \times 7$

Step3: Simplify the expression

First, $\frac{135}{360} = \frac{3}{8}$. Then:
$L = \frac{3}{8} \times 14\pi = \frac{42\pi}{8} = 5.25\pi$
Approximate $\pi \approx 3.14$, so $L \approx 5.25 \times 3.14 = 16.485$

Answer:

A. 16.5 in