The volume of a box with a rectangular base is 3072 cm3. the length of the side are in the ratio 1:2:3. calculate the length of the shortest side

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.