Joe-Ann has several little cubes. She joins the cubes using a drop of glue for each pair of faces in contact to each other. She made a cube with eight little cubes and used drops of glue. She made a cube with twenty-seven little cubes and used drops of glue.
If she wants to make a cube with a thousand little cubes how many drops of glue will she use?
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Every face that is not on the surface of the cube gets a drop of glue, and ever drop of glue attaches two faces. Thus we have: faces per glue drop total faces − exterior faces = 2 6 × number of cubes − surface area = 2 6 0 0 0 − 6 0 0 = 2 7 0 0