Question

in circle o, the length of radius ol is 6 cm and the length of arc lm is 6.3 cm. the measure of angle mon is 75°. rounded to the nearest tenth of a centimeter, what is the length of arc lmn?
7.9 cm
10.2 cm
12.6 cm
14.2 cm

Explanation:

Step1: Find arc MN length

Arc length formula: $s = \frac{\theta}{360^\circ} \times 2\pi r$
Substitute $\theta=75^\circ$, $r=6$ cm:
$s_{MN} = \frac{75^\circ}{360^\circ} \times 2\pi \times 6$
$s_{MN} = \frac{5}{24} \times 12\pi = 2.5\pi \approx 7.85$ cm

Step2: Sum arcs LM and MN

Total arc length $s_{LMN} = s_{LM} + s_{MN}$
Substitute $s_{LM}=6.3$ cm, $s_{MN}\approx7.85$ cm:
$s_{LMN} = 6.3 + 7.85 = 14.15$ cm

Step3: Round to nearest tenth

$14.15 \approx 14.2$ cm

Answer:

14.2 cm