Answer
$\dfrac{\pi^2}{2}$
Work Step by Step
Since, the vertical slices solid are circular discs , so we will use the disk method to compute the volume of revolution of the curve.
The volume of revolution of the curve can be expressed as: $V=\pi \int_p^q [f(x)]^2 dx\\=\pi \int_{-1}^{1} (\dfrac{1}{\sqrt {1+x^2}})^2 \ dx \\= 2 \pi \int_0^1 \dfrac{1}{1+x^2} \ dx \\= 2 \pi [\tan^{-1} (1) -\tan^{-1} (0)] \\=2\pi (\dfrac{\pi}{4}-0) \\=\dfrac{\pi^2}{2}$
