A metallic cube of side 12 cm is cut into 8 equal solid cubes of equal volume. Find the ratio between the surface areas of a cube with a larger edge to a smaller edge.
4 : 1
The side of the original cube is 12 cm, and it is cut into 8 smaller cubes, so each smaller cube has a side of:
Side of smaller cube = 12 / 2 = 6 cm
Now, the surface area of a cube is given by the formula: Surface area = 6 × side2
Surface area of the larger cube (side = 12 cm):
Surface area = 6 × 122 = 6 × 144 = 864 cm2
Surface area of the smaller cube (side = 6 cm):
Surface area = 6 × 62 = 6 × 36 = 216 cm2
Thus, the ratio of the surface areas is:
Surface area ratio = 864 / 216 = 4 : 1
The ratio between the surface areas of a cube with a larger edge to a smaller edge is 4 : 1.
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