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If the height of a cube doubles and becomes a square prism instead of a cube, four of the six original equal area surfaces double in area, but the other two are unchanged. Therefore the area of the square prism is (2/3) X 2 = 4/3 as great as the original cube.

If the original object is to remain a cube when its height doubles, all the other dimensions must also double; in that instance, the area increases by a factor of four.

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Q: What happens to the surface area of a cube as its height doubles?
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