Unit 5, Lesson 8
Speaking of Scaling
Geometry
8.1
Warm-up
Going Backward
The image shows a cone that has a base with an area of
What was the scale factor of the dilation?
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The image shows a cone that has a base with an area of
What was the scale factor of the dilation?
Suppose a solid is dilated. If we know the factor by which the surface area or volume scale changed, we can work backward to find the scale factor of dilation. Then we can use that information to solve problems.
A company sells 10 inch by 10 inch by 14 inch 5-gallon aquariums, but a museum wants to buy a 135-gallon aquarium with the same shape. The company needs to know the dimensions of the new tank and by what factor the surface area will change.
Gallons are a measure of volume. So, the volume of the tank increases by a factor of
|
original aquarium |
dilated aquarium |
|
|---|---|---|
| height (inches) | 10 | |
| length (inches) | 14 | |
| width (inches) | 10 | |
| surface area (square inches) | 760 | |
| volume (gallons) | 5 |
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