(Solved): The figure shows a solid whose horizontal cross section at height \( y \) is a circle of radius \( ...

The figure shows a solid whose horizontal cross section at height \( y \) is a circle of radius \( 4(1+y)^{-2} \) for \( 0 \leq y \leq H \). Find the volume, \( V \), of the solid. (Express numbers in exact form. Use symbolic notation and fractions where needed.)