jmc

The volume is proportional to the square of the base radius and to the height, so if these have the same volume, their heights are inversely proportional to the square of the radii. This means that with a radius 1/3 as big as the first, the second cone has a height of $24{\left(\frac{1}{1/3}\right)}^2=24\cdot 9=\boxed{216}$ inches.