Two solids are said to be similar if they have the same shape and their corresponding sides are in proportion. The ratio of the corresponding linear dimensions (lengths, widths, heights) of two similar solids is called the scale factor. Theorem 11-12 states that the ratio of the areas of two similar figures is equal to the square of the scale factor, and the ratio of the volumes of two similar solids is equal to the cube of the scale factor.
Theorem 11-12 states that if two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding side lengths, and the ratio of their surface areas is equal to the square of the ratio of their corresponding side lengths.
