Scale Factors of 3-D Objects
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D. Scale Factors of 3-D Objects
The large grey cube shown in the image above is made up of a number of
smaller, yet similar, cubes. The large grey cube has dimensions 3 units
by 3 units by 3 units. The red cube has dimensions 1 unit by 1 unit by 1
unit. The large grey cube and the red cube are similar because each
dimension of the large grey cube is three times larger than the
corresponding dimension of the red cube. In other words, the scale
factors are the same for all corresponding dimensions.
If two objects are similar, the scale factors will be the same for all corresponding lengths.
Example 1
Replacing heart valves in humans is now so common that a gibbon (an ape) will receive its first heart valve replacement within the next 10 years.
A human heart valve has a diameter of 0.2 mm and a height of 15 mm. If a gibbon's heart is 
the size of a human heart, what are the diameter and height of a gibbon's heart valve?
Multiply the dimensions given for a human heart by the scale factor of to find the dimensions of a gibbon's heart valve.
| Diameter of a human heart valve = 0.2 mm |
Diameter of a gibbon's heart valve:
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| Height of a human heart valve = 15 mm |
Height of a gibbon's heart valve:
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- The gibbon's heart valve has a diameter of 0.04 mm and a height of 3 mm.
- These dimensions are reasonable because both the diameter and height of a gibbon's heart valve are proportionately smaller than those of a human. Compared to a human heart, a gibbon's heart is a reduction.
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