Question

in circle m, diameters jl and hk each measure 16 centimeters.
what is the approximate length of minor arc jh? round to the nearest tenth of a centimeter.
○ 3.5 cm
○ 6.9 cm
○ 21.6 cm
○ 46.8 cm

Explanation:

Step1: Find the circle's radius

The diameter is 16 cm, so radius $r = \frac{16}{2} = 8$ cm.

Step2: Identify arc's central angle

Vertical angles are equal, so the central angle for arc JH is $25^\circ$.

Step3: Calculate arc length

Use the arc length formula $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta=25^\circ$, $r=8$ cm.
$L = \frac{25^\circ}{360^\circ} \times 2\pi \times 8$
$L = \frac{25}{360} \times 16\pi$
$L = \frac{400\pi}{360} \approx \frac{400 \times 3.1416}{360} \approx 3.5$ cm

Answer:

3.5 cm