Question

# The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of pi and then round to two decimal places.

Analytic geometry
The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of $$\displaystyle\pi$$ and then round to two decimal places.

2021-02-27
1. A complate revolution measures $$\displaystyle{2}\pi$$ radians. The minute hand moves $$\displaystyle\frac{{1}}{{3}}$$ of a complete revolution.
2. $$\displaystyle\theta=\frac{{1}}{{3}}{\left({2}\pi\right)}=\frac{{{2}\pi}}{{3}}$$ radians
3. r = inches
4. $$\displaystyle{s}={r}\theta={\left({6}\in\right)}{\left(\frac{{{2}\pi}}{{3}}\right)}={4}\pi$$
5. $$\displaystyle{4}\pi\approx{12.57}$$