Question

question 6 of 10
in the diagram below, what is the approximate length of the minor arc \\(\overarc{ab}\\)?
(diagram: a circle with center c, radius 10 cm, angle \\(\angle acb = 90^\circ\\), points a and b on the circle)
options:
a. 31.4 cm
b. 14.3 cm
c. 7.9 cm
d. 15.7 cm

Explanation:

Step1: Identify arc length formula

Arc length = $\frac{\theta}{360^\circ} \times 2\pi r$
$\theta=90^\circ$, $r=10$ cm

Step2: Substitute values

$\frac{90^\circ}{360^\circ} \times 2 \times \pi \times 10 = \frac{1}{4} \times 20\pi = 5\pi$

Step3: Calculate approximate value

$5\pi \approx 5 \times 3.14 = 15.7$ cm

Answer:

D. 15.7 cm