Cube Riddle
The solid above is composed of unit cubes. It has a volume of 8 units cubed and a surface area of 24 units squared.
Is there a solid composed of unit cubes such that the numbers corresponding to volume and surface area are equal to each other?
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1 solution
We can accomplish our goal with the unit cubes assembling a larger cube.
With sides each of length x , the volume is x 3 and the surface area is 6 x 2 . We want them equal, that is, x 3 = 6 x 2 . This happens when x 3 − 6 x 2 = 0 or ( x 2 ) ( x − 6 ) = 0 .
The factor x − 6 means x = 6 is a solution, so a 6 by 6 by 6 cube will have the same surface area and volume.