Geometry 12.7 Similar Solids
Similar solids - two solids with equal ratios of corresponding linear measures, such as heights or radii.
Common ratio is called the scale factor.
Example:
If a rectangular prism has sides of 3, 2, and 2, and a second one has lengths of 5, 4, and 4, are these two solids similar?
Set up ratios:
3/6 = 2/4 = 2/4
1/2 = 1/2 = 1/2 , so yes they are.
If 2 similar solids have a scale factor of a:b, then the corresponding areas have a ratio of a2:b2 and corresponding volumes have a ratio of a3:b3.
Example:
If one sphere has a volume = 8pi and a second one has a volume of 125pi, what is the ratio of their areas?
((8pi)/(125pi))1/3 = 2/5
(2/5)2 = 4/25
Example:
The scale factor of the model car is 1:16. If the model car is 5.5 in. What is the height of the car?
1/16 = 5.5/x
x = 88 inches
Homework: Worksheet 12.7 B
