Answer
$\frac{\pi}{3}$ radians
Work Step by Step
The passing of the hour hand between $1$ o'clock and $3$ o'clock represents a time of two hours.
Since $12$ hours represent $2\pi$ radians, 2 hours represent $x$ radians. Using ratios and cross multiplying:
$\frac{12}{2\pi}=\frac{2}{x}$
$12x=4\pi$
$x=\frac{4\pi}{12}$
Simplifying, $x=\frac{\pi}{3}$ radians
Therefore, the pass of the hour hand between $1$ o’clock and
$3$ o’clock represents $\frac{\pi}{3}$ radians.
