similar shapes have corresponding angles that are equal. Also, any length in one shape is equal to the scale factor times the corresponding length in the other shape.
Those would be called similar solids.
These are solids whose corresponding sides are in the same proportion, and all its angles are equal.
The ratio of the volumes of two similar solids is proportional to the cube of the diameter - or of any other linear measurement. For example, at twice the diameter, you would have 8 times the volume.
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The ratio of the volumes of similar solids is (the ratio of their linear dimensions)3 .