Extend the sloping sides to the apex. Let the removed small cone have height h. Similarity gives \(h/(h+12.7)=9.9/13.2=3/4\), so \(h=38.1\text{ cm}\) and the large cone height is \(50.8\text{ cm}\).

\(V=\frac13\pi(13.2)^2(50.8)-\frac13\pi(9.9)^2(38.1)=5358.730828\ldots\text{ cm}^3\). Thus \(\boxed{5360\text{ cm}^3}\) to 3 significant figures.