Answer
$\pi$
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: $V=\pi \int_p^q [f(x)]^2 dx\\=\pi \int_{0}^{\pi/4} \sec^2 x \ dx \\= \pi [\tan (x) ]_0^{\pi/4} \\= \pi [\tan (\dfrac{\pi}{4})-\tan (0)] \\=\pi (1-0) \\=\pi$
