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let a= side of the cube

area of one face is a2 so area of the cube is 6 x a2

so if the dimension is doubled the new dimension is 2a

therefore area of the new face would be (2a)2 or 4a2 and of that cube is 6 x 4a2 now if we divide the two areas 24a2/6a2 the answer would be 4 therefore if we double the dimension of a cube the area will be 4 times bigger.

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