Answer
$$\pi(\dfrac{\pi}{2}-1)$$
Work Step by Step
We need to integrate the integral to compute the volume.
We have:
Area $=\pi r^2=\pi (1-\tan^2 y)$
$$Volume = \pi \times \int_{0}^{\pi/4} (1- \tan^2 (y) ) \space dy \\= \pi (y-(\tan y -y)]_{0}^{\pi/4 } \\= \pi [2y-\tan (y) ]_{0}^{\pi/4} \\=\pi(\dfrac{\pi}{2}-1)$$
