Similar Solids – solids with the same
shape but not necessarily the same
size.
To determine if solids are similar, determine if
all corresponding lengths are in the same
proportion.
In prisms, you can also determine if bases are
similar (since they are plane figures).
All spheres and cubes are similar.
Right Cylinders
6
Bases are similar because
all circles are similar.
Heights are in the same
proportion.
4
Cylinder A
12
Cylinder B 8
Scale Factor = 3:2
Not Similar
10
9
15
12
12
9

15
10
Lengths are not
proportional.
Using these cylinders:
6
4
Cylinder A
12
Cylinder B 8
Determine the following values and ratios
Find the ratio of the Base Perimeters, Base Areas,
Lateral Areas, Total Areas and Volumes.
Cylinder A
Cylinder B
Ratio of A:B
12π
8π
3:2
36π
16π
9:4
Lateral Areas
144π
64π
9:4
Total Areas
216π
96π
9:4
432π
128π
27:8
Base Perimeters
Base Areas
Volumes
Theorem 12-11:
If the scale factor of two similar solids is a:b, then
•The ratio of the corresponding
lengths and base perimeters is a:b
•The ratio of the areas (base areas,
lateral areas, total areas) is a²:b²
•The ratio of the volumes is a³:b³
Example 1: Two similar prisms have a scale
factor of 4:7. Find the ratio of the lateral area
and volume.
Lateral Areas = 16:49
Volumes = 64:343
Example 2: The total areas of two spheres are
144 and 4. Find the ratio of their volumes.
Total Areas = 144π:4π = 36:1
Scale Factor = 6:1
Ratio of Volumes = 216:1
Example 3: Two similar square pyramids have
base areas 4m² and 36m². Find the ratio of the
heights of the pyramids.
Base Areas = 4:36 = 1:9
Scale Factor = 1:3
Ratio of Heights = 1:3
If the height of the larger pyramid is 27m, what
is the height of the smaller pyramid?
1
x

3 27
Height of
= 9m
Smaller
Pyramid