Two solids are similar if and only if they are the same type of solid and their corresponding linear measures (radii, heights, base lengths, etc.) are proportional.
When two 2-D shapes are similar, the ratio of the area is a square of the scale factor. When two solids (3-D shares) are similar with a scale factor of a, the surface areas are in a ratio of (a)2.
When two solids are similar with a scale factor of a, then the volumes are in a ratio of (a)3.