Answer
a. $s^2h$
b. $s^2h$
Work Step by Step
a. Step 1. Draw a diagram as shown in the figure. Assuming the line $L$ is the $x$-axis, the limits of integration with respect to $x$ can be found from $x_0$ to $x_0+h$, where $x_0$ is the starting point and $h$ is the amount of movement along the $x$-axis.
Step 2. The cross section is a square with a side length of $s$; we have $dV=s^2\ dx$. Here, we have approximated the infinite small volume as a rectangular prism even with the rotation because the rotation has a limited angle (one turn or a few turns) while $dV$ can be infinitely small.
Step 3. Letting $x_0=0$, we have $V=\int_0^h s^2\ dx=s^2(x)|_0^h=s^2h$
b. Based on the discussions above, the volume will be the same for limited turns -- that is, $V=s^2h$.
