If s is the length of an edge, then
the surface area of the cube = 6s² square centimeters, and
the volume of the cube = s³ cubic centimeters.
The number of cubic centimeters in the volume of the cube is equal to twice
the number of square centimeters in its surface area, so:
s³ = 2∙6s²
s³ = 12s²
s³ - 12s² = 0
s²(s - 12) = 0
s² = 0; s - 12 = 0
s = 0 s = 12
We ignore the humorous answer, s = 0 (which says that a cube reduced to a
point has 0 volume and 0 surface area, and 0 is indeed twice 0, lol).
Now seriously, a cube that has each edge measuring 12 centimeters has
12³ = 1728 cubic centimeters of volume and 6∙12² = 864 square centimeters of
surface area. Sure enough, 1728 is twice 864.
Answer: 1728
Edwin
