Answer
$$2.3014$$
Work Step by Step
We need to integrate the integral to compute the volume.
$$Volume= \pi \int_{0}^{\pi/4} \pi (\sqrt 2-\sec x \tan x)^2 \space dx \\=\pi \int_{0}^{\pi/4} (2- 2\sqrt 2 \sec x \tan x+\tan^2 x \sec^2 x) \space dx \\=(\pi) [2x-2\sqrt 2 \sec x+(\dfrac{1}{3}) \tan^3 x)]_0^{\pi/4} \\=2.3014$$
