6. The volume of the solid of revolution obtained by rotating the figure bounded by the curves $x^{2}=4 y, x^{2}=-4 y, x=4, x=-4$ around the $y$-axis is $V_{1}$: The volume of the solid of revolution obtained by rotating the figure composed of points $(x, y)$ that satisfy $x^{2} y \leqslant 16 \cdot x^{2}+(y-2)^{2} \geqslant 4 \cdot x^{2}+(y+2)^{2} \geqslant 4$ around the $y$-axis is $V_{2}$, then
A. $V_{1}=\frac{1}{2} V_{2}$
B. $V_{1}=\frac{2}{3} V_{2}$
C. $V_{1}=V_{2}$
D. $V_{1}=2 V_{2}$
6. C The two solids of revolution obtained by rotating the figures around the $y$-axis are confined between two parallel planes that are 8 units apart,

When intersected by any plane perpendicular to the $y$-axis, with the distance from the section to the origin being $|y|$, the areas of the resulting sections are $S_{1}=\pi\left(4^{2}-4|y|\right)$ and $S_{2}=\pi\left(4^{2}-y^{2}\right)-\pi\left[4-(2-|y|)^{2}\right]=\pi\left(4^{2}-4|y|\right)$.
Therefore, $S_{1}=S_{2}$.
By the principle of Cavalieri, the volumes of the two solids are equal, so $V_{1}=V_{2}$.