find the height of largest right circular cone that can be cut out of a cube whose volume is 729 cm^3.

Volume of the cube = 729 cm³
Let s = edge of the cube
$$\begin{gathered} \Rightarrow s^3 = 729 \\ \Rightarrow s = 9 \mathrm{cm} \end{gathered}$$
Height of the cone = Length of the edge of the cube = 9 cm