Answer
$12 \pi$
Work Step by Step
$Volume=\iint_{x^2+y^2 \leq 4} \int_{0}^{3-y} dz dA$
$\implies Volume=\iint_{x^2+y^2 \leq 4} (3-y) dA $
$\implies Volume=3 \iint_{x^2+y^2 \leq 4} dA - \iint_{x^2+y^2 \leq 4} y dA$
Since, the inner integral is the integral of the odd continuous function in symmetric interval, this means that $\iint_{x^2+y^2 \leq 4} y dA=0$
Thus, $Volume=(3) \times (\pi) \times (2)^2 -0=12 \pi$
