Answer
$12 \pi$
Work Step by Step
$Volume; V=4 \int_0^{2} \int_{0}^{\sqrt {4-x^2}} \int_{0}^{4-x^2} \ dz \ dy \ dx$
or, $=4 \int_0^{2} \int_{0}^{\sqrt {4-x^2}} (4-x^2) \ dy \ dx$
or, $=4 \int_0^{2} (4-x^2)^{3/2} \ dx$
or, $= [x (4-x^2)^{3/2} +6x \sqrt {4-x^2}+24 \sin^{-1} (\dfrac{x}{2}) ]_0^{2}$
or, $=24 \arcsin(1)$
or, $=12 \pi$
