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 [latex]k=1[/latex], then the two solids are congruent; one is a reproduction of the other.
- If [latex]0< k< 1[/latex], then prism B is a reduction of prism A;
- If [latex]k> 1[/latex], 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.
