Question

The minute hand of a clock is 9 inches long. how far does the tip of the minute hand move in 40 minutes​

Answer 1

$\text{The minute hand of a clock is 9 inches long.}\\ \text{we need to find the distance traveled by the tip of the minute }\\ \text{hand moved in 40 minutes.}$

$\text{That is we need to find the length of the arc formed by the minute}\\ \text{hand in 40 minutes. We know that in one complete revolution of the}\\ \text{minute hand there are 60 minutes. so the central angle formed by the }\\ \text{minute hand in 40 minutes is}=\frac{40}{60}*2\pi =\frac{4\pi}{3} \text{ radians}\\ \\ \text{hence using the arc length formula, }s=r\theta, \text{ we get}\\ \\ \text{distance traveled by the tip}=9\times \frac{4\pi}{3}=12\pi\approx 37.7 \text{ inches}$

Hence the tip of the minute hand moved approximately 37.7 inches in 40 minutes.