Alex has 64 cubes, with the dimensions in ft (1/2) he uses all the cubes to fill a box shaped like a larger rectangular prism. there are no gaps between the cubes. A. what is the volume, in cubic feet, of the larger rectangular prism?B. what is the possible set of dimensions , in feet, of the larger rectangular prism?

A) First, find the volume of each cube:
V = s³
   = (1/2)³
   = 1/8 ft³

We have a total of 64 cubes, therefore the maximum volume will be:
Vmax = 64 · (1/8) = 8 ft³

B) The volume of a rectangular prism is given by:
V = w × l × h
Therefore any combination of w × l × h = Vmax = 8 will be fine.
Examples:
2 × 2 × 2
4 × 2 × 1