Similarity (geometry) - Galileo's Square-cube Law

Galileo's Square-cube Law

The ratio between the areas of similar figures is equal to the square of the ratio of corresponding lengths of those figures (for example, when the side of a square or the radius of a circle is multiplied by two, its area is multiplied by four — i.e. by two squared).

The ratio between the volumes of similar figures is equal to the cube of the ratio of corresponding lengths of those figures (for example, when the edge of a cube or the radius of a sphere is multiplied by two, its volume is multiplied by eight — i.e. by two cubed).

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