Let’s see what happens to volume and weight as we increase the dimensions of a cube.
Width = 10 cm
Length = 10 cm
Height = 10 cm
Volume (Length x Width x Height) = 10 cm x 10 cm x 10 cm = 1000 cm3
Width = 20 cm
Length = 20 cm
Height = 20 cm
Volume (Length x Width x Height) = 20 cm x 20 cm x 20 cm = 8000 cm3
While the dimensions of Cube 2 are only double the dimensions of Cube 1, the volume of Cube 2 has increased 8-fold!
The weight of a growing cube increases at a faster rate than its dimensions. If each cubic centimeter weighs one gram, then Cube 1 weighs 1000 grams, Cube 2 weighs 8000 grams, and a third cube twice the size of Cube 2 would weigh 64,000 grams. Volume (and hence, weight!) increases faster than the dimension of a single side of the cube does.
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