Similar Figures
Scale Factor

The previous example allowed you to explore the relationship between the scale factor of a dilation to the volume of its image. If the similarity ratio of two similar figures is r:t, then the ratio of their volumes is r3:t3.

Example  Given the two figures below, if the volume of the first cylinder is 283 mm 3, what is the volume of the second cylinder?

sim ex

Step 1.  Find the similarity ratio of the cylinders.

sim ratio

Step 2.  Find the similarity ratio for the volume of the cylinders.

vol ratio

Step 3.  Use a proportion to find the volume of the second cylinder.

proportion

 

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