11.9. Area and Volume of Similar Solids http://www.ck12.org
Surface Area Ratio:If two solids are similar with a scale factor ofab, then the surface areas are in a ratio of
(a
b) 2
.
Volume
Let’s look at what we know about similar solids so far.
TABLE11.2:
Ratios Units
Scale Factor ab in, ft, cm, m, etc.
Ratio of the Surface Areas(a
b) 2
in^2 ,f t^2 ,cm^2 ,m^2 ,etc.
Ratio of the Volumes ?? in^3 ,f t^3 ,cm^3 ,m^3 ,etc.It looks as though there is a pattern. If the ratio of the volumes follows the pattern from above, it should be the cube
of the scale factor.
Volume Ratio:If two solids are similar with a scale factor ofab, then the volumes are in a ratio of
(a
b) 3
.
Example A
Are the two rectangular prisms similar? How do you know?
Match up the corresponding heights, widths, and lengths to see if the rectangular prisms are proportional.
small prism
large prism=
3
4. 5
=
4
6
=
5
7. 5
The congruent ratios tell us the two prisms are similar.
Example B
Two similar cylinders are below. If the ratio of the areas is 16:25, what is the height of the taller cylinder?