Finding out the amount of volume through integration

A right circular cone has height 4 cm and base radius 2. It is over-filled with ice cream,

in the usual way. Place the cone so its vertex is at the origin, and its axis lies along the

positive y–axis, and take the cross-section containing the x–axis. The top of this crosssection

is a piece of the parabola y = 8 − x^2 . The whole filled ice-cream cone is obtained

by rotating this cross-section about the y–axis.

What is the volume of the ice cream?