*

measurements in comparable Figures snucongo.org Topical synopsis | Geometry overview | MathBits" Teacher resources Terms of Use call Person: Donna Roberts

Once we know that two figures are similar, we likewise know extr information about specific measurements entailing these figures.

You are watching: The ratio of the volumes of two similar solid


If two polygons space similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and also perimeters room all in the very same ratio. (Note that these are all "length" measurements.) In comparable figures, if the ratio of any type of of these matching lengths is expressed as ,then the ratio of the other matching lengths can also be expressed together .


Example: If the corresponding sides of two similar triangles space in the proportion 2:5, what is the ratio of their perimeters? Answer: 2:5


If two polygons space similar, the ratio of their areas is same to the square of the proportion of their matching sides. (Note the area is no a "length" measurement - it is a surface "area" measurement.)

In comparable figures, if the ratio of two corresponding sides (or other lengths) is expressed as ,then the proportion of the areas can be expressed as

*
.


Example: If the matching sides that two comparable triangles are in the ratio 3:7, what is the ratio of their areas? Answer: 9:49


If two solids space similar, the ratio of their volumes is same to the cube that the proportion of their matching sides.

See more: How Many Amps Is A Microwave ? Learn Here

(Note the volume is no a "length" measure up - the is a 3-D measurement.)

In similar figures, if the ratio of two matching sides (or various other lengths) is expressed together ,then the ratio of the volumes can be to express as

*
.


Example: If the political parties of two cubes room in the proportion 2:3, what is the ratio of their volumes? Answer: 8:27


Topical outline | Geometry overview | snucongo.org | MathBits" Teacher sources Terms the Use call Person: Donna Roberts