Two solid right circular cones have the same height. The radii of their bases are \(a\) and \(b\). They are melted and recast into a cylinder of same height. The radius of the base of the cylinder is ______ ?
Volume of first cone = pi (a)^2 h / 3
Volume of second cone = pi (b^2) h / 3
Volume of cylinder = combined volumes of cones = pi * h ( a^2 + b^2) / 3
pi * r^2 * h = pi * h ( a^2 + b^2) / 3
r^2 = (a^2 +b^2) / 3
r = sqrt [ (a^2 +b^2) / 3 ] = radius of the cylinder