Question

The minute hand on a clock is 10 centimeters long and travels through an arc of 108° every 18 minutes.121110108°-9238476 5Which measure is closest to the length of the arc the minute hand travels through during this 18-minute period?O 3 cmO 6 cmO 9.4 cmcheO 18.8 cm

Answer 1

The formula for the length of an arc(l) is,

$l=\frac{\theta}{360^0}\times2\pi r$

Given data

$\begin{gathered} \theta=108^0 \\ \pi=3.14 \\ r=\text{radius}=10\operatorname{cm} \end{gathered}$

Solving for the length of the arc

$\begin{gathered} l=\frac{108^0}{360^0}\times2\times3.14\times10cm \\ l=0.3\times2\times3.14\times10\operatorname{cm} \\ l=18.84\operatorname{cm}\approx18.8\operatorname{cm}(\text{nearest tenth)} \\ \therefore l=18.8\operatorname{cm} \end{gathered}$

Hence, the length of the arc is 18.8cm.

The correct option is Option D.