Answer
$$\dfrac{13}{24}$$
Work Step by Step
$Volume=\int_{0}^{ \pi/2 }\int_{0} ^{1}\int_{0} ^{2-r \sin \theta } r^2 \cos \theta \space dx \space dr \space d\theta $
or, $=\int_{0}^{ \pi/2}\int_{0} ^{1} 2 r^2 \cos \theta - r^3 \cos \theta \sin \theta dr d\theta $
or, $=\int_{0}^{ \pi/2}\int_{0} ^{1} (2/3) \cos \theta -(\dfrac{1}{4}) \cos \theta \sin \theta d\theta $
Let $\sin \theta =a$ and $\cos \theta d\theta =da$
Now, $Volume =\dfrac{2}{3} \times |\sin \theta|_0^{\pi/2} - \dfrac{1 }{4} \int_0^1 a da $
or, $Volume=\dfrac{2}{3}-\dfrac{1}{8}=\dfrac{13}{24}$
