The volume of the box is 3072 cm^3.
Getting the dimensions given the ratio 1:2:3, we can formulate the equation deriving it from the formula of the volume of the box:
Volume = l w h
Volume = 1x 2x 3x
3072 = 1x 2x 3x
3072 = 6x^3
x^3 = 512
x = cube root (512)
x = 8 cm
2x = 16 cm
3x = 24 cm
So the shortest side is 8cm.
