Chapter 6: Applications of Definite Integrals - Practice Exercises - Page 363: 14

$2 \pi (4 -\pi) $

We need to use the shell model as follows: $V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dx$ $ \implies V= \int_0^{\pi/4} (2 \pi) (4) (tan^2 x) dx$ or, $=8 \pi \times \int_0^{\pi/4} (\sec^2 x-1) dx$ or, $=8 \pi [\tan x-x] _0^{\pi/4}$ or, $= 2 \pi (4 -\pi) $