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A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface




Volume of original cube=12*12*12=1728 cm^3. therefore volume of smaller cubes=216 cm^3.
so, length of side of smaller cube = cube root of 216 = 6 cm. surface area of original cube = 6a^2=6*12*12=864 cm^2. surface area of one of the smaller cubes=6*6*6=216 cm^2. therefore total surface area of all the smaller cubes = 8*216 = 1728 cm^2. hence ratio of surface areas = 864 / 1728 = 1/2. 
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