Answer :
[tex]V_1=36\pi\ cm^3\\\\V_2=288\pi\ cm^3\\\\\frac{V_2}{V_1}=k^3\ \ \ (k-similar\ scale)\\\\k^3=\frac{288\pi}{36\pi}\\\\k^3=8\\\\k=\sqrt[3]8\\\\k=2[/tex]
[tex]the\ base\ radius\ of\ the\ smaller\ cone\ is\ 3cm\\\\the\ base\ radius\ of\ the\ bigger\ cone\ i\ 2\cdot3cm=6cm[/tex]
[tex]the\ base\ radius\ of\ the\ smaller\ cone\ is\ 3cm\\\\the\ base\ radius\ of\ the\ bigger\ cone\ i\ 2\cdot3cm=6cm[/tex]