Answer
$\pi ( 3 \pi -8)$
Work Step by Step
We integrate the integral to calculate the volume as follows:
$V= \int_{0}^{\pi/2} \pi (2-2 \sin x)^2 dx$
Now, $V= \int_{0}^{\pi/2} \pi (4- 8 \sin x+4(\sin x)^2) dx$
or, $= \int_{0}^{\pi/2} 4\pi (1-2 \sin x+\dfrac{1-\cos 2x}{2}) dx$
or, $=4 \pi(\dfrac{3x}{2} +2 \cos x-\dfrac{\sin (2x)}{4})$
Set $x=0 \space to \space \dfrac{\pi}{2}$
So, $V=\pi ( 3 \pi -8)$
