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
ANSWERED
asked 2021-02-26
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.

Answers (1)

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. \(\displaystyle{4}\pi\approx{12.57}\)
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