Calculus cross sections help

Consider the straight cone of height 6 whose base is the circle of radius 2. Find the smaller of the volumes of the two solids obtained by cutting the cone with a plane through the vertex of the cone and the line in base which has distance sqrt(2) to the center of the base.

Thanks!

V = 2(π - 2) cubic units;

check the following sketch
http://i1321.photobucket.com/albums/u552…