1. Similar Solids 12.7

2. definition Similar Solids Two solids in which their corresponding linear measures form equal ratios. 4 3 6 4.5 3 5 9 5.4 4 6 3 4.5 = 3 5.4 5 9 =

3. theorem Similar Solids If two similar solids have a scale factor of a:b, then ratio of their areas is a 2 :b 2 and ratio of their volumes is a 3 :b 3. 4 6 3 4.5 scale factor area ratio volume ratio 4343 16 9 64 27

4. examples Are the two solids similar? 12 8 6 6 2 4 = ? = ? No 12 6 8484 6262

5. example Are the two solids similar? 5 3 2 2.5 1.5 1 = ? = ? Yes 5 2.5 2121 3 1.5

6. example The two prisms are similar. Find the surface area of the smaller prism. 5 3 2 1 scale factor area ratio 2121 4141

7. example 5 3 2 1 8181 The two prisms are similar. Find the volume of the smaller prism. scale factor volume ratio 2121