Answer: The scale factor is 3
Divide the two volumes (larger over small) to find that (21870pi)/(810pi) = 27. This means that the larger volume is 27 times bigger than the smaller volume.
From here, you apply the cube root to this result to get 3. Note how 3 cubed = 3^3 = 3*3*3 = 27.
The linear scale factor is 3. The larger figure has a radius 3 times larger than its counter part in the smaller cone. The same applies to the heights as well.