Number of hours in a clock $= 12$ hours
One rotation hour hand covers $360^{\circ} $
$360$ degrees $= 12$ hours
$1$ degree $=\dfrac{12}{360}$ hours
$225$ degrees $=\dfrac{12}{360}\times 225$ hours $=7.5$ hours
$(OR)$
The worker stays in the factory $=3\ hours \ ({0^{\circ} \ to \ \ 90^{\circ}}) +3 \ hours \ ({90^{\circ} \ to \ \ 180^{\circ}}) +\dfrac{3}{2}\ hours \ ({180^{\circ} \ to \ \ 225^{\circ}}) = 7.5 \ hours$
So, option $(D)$ is the correct choice.