The base of a solid is the region enclosed by $y= \frac{-x^2}{4}+4$ and $y=0$. Find the volume.

The base of a solid is the region enclosed by $y= \frac{-x^2}{4}+4$ and $y=0$. Cross-sections perpendicular to the $y$-axis are rectangles with heights twice that of the side in the $xy$-plane.