# Similar Solids

## Similar Solids

Two solids are similar if one is an enlargement, a reduction or a reproduction of the other.

### Properties

• All cubes are similar solids.
• All spheres are similar solids.
• The corresponding lengths in similar solids are proportional.

### Example

The dimensions of prism A are : a, b and c.

The dimensions of a similar prism B are : ka, kb and kc.

The ratio of similarity is k :

• If $$k=1$$, then the two solids are congruent; one is a reproduction of the other.
• If $$0< k< 1$$, then prism B is a reduction of prism A;
• If $$k> 1$$, then prism B is an enlargement of prism A.

The volume of solid B is equal to the volume of solid A multiplied by the cube of the ratio of similarity k.

The area of solid B is equal to the area of solid A multiplied by the square of the ratio of similarity k.