Two similar boxes A and B are given with box B created by dividing box A's dimensions by 2.
Recall that the scale factor, k is the ratio of lengths of two corresponding sides of similar figures.
Since the dimensions of A were divided by 2 to form B, it follows that the scale factor of box A to box B is:

Also, recall the Similar Solids Theorem
It follows that the ratio of the volumes of the given solids is:

Let the volume of box A be V₁ and let the volume of box B be V₂, it, therefore, implies that:

Substitute the value for the volume of box A into the equation, V₁=64:

Hence, the volume of box B is 8 m³.