1. 12-7 Similar Solids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2. Warm Up Classify each polygon. 1. A square has a side 4 cm, a similar larger square has a length of 20 cm. Provide the perimeter ration. 2. Use problem 1 to provide the length ratio. 3. Now the answer in problem 2 to provide the scale factor (unit ratio): Perimeter Ratio  16:80 Length Ratio:  4:20 Unit Ration:  1:5 12.7 Similar Solids  1:5

3. Find and Use the scale factor of Similar Solids Use Similar Solids to solve real-life problems. Objectives 12.7 Similar Solids

4. Similar Solids Vocabulary 12.7 Similar Solids

5. Similar Solids Two solids of the same type with equal ratios of corresponding linear measures (such as heights or radii) are called similar solids.

6. 12.7 Similar Solids Similar solidsNOT similar solids

7. 12.7 Similar Solids Similar Solids & Corresponding Linear Measures 12 3 6 8 2 4 Length: 12 = 3 width: 3 height:6 = 3 Notice that all ratios for corresponding measures are equal in similar solids. The reduced ratio is called the “scale factor”. To compare the ratios of corresponding side or other linear lengths, write the ratios as fractions in simplest terms. 8 2 2 4 2

8. Example 1A: Are these Solids Similar 12.7 Similar Solids 16 12 8 6 9

9. Example 1A: Are these Solids Similar 12.7 Similar Solids 16 12 8 6 1212 9 All corresponding ratios are equal, so the figures are similar Solution:

10. Example 1B: Decide if the solids are Similar. 12.7 Similar Solids 8 18 4 6

11. Example 1B: Classifying Three-Dimensional Figures 12.7 Similar Solids 8 18 4 6 Corresponding ratios are not equal, so the figures are not similar Solution:

12. 12.7 Similar Solids If two similar solids have a scale factor of a : b, then corresponding areas have a ratio of a 2 : b 2. This applies to lateral area, surface area, or base area. Length/Perimeter ratio  a:b Area Ratios  a 2 : b 2 Similar Solids and Ratio of Areas

13. 12.7 Similar Solids 10 4 8 Surface Area = base +lateral = 40 + 108 = 148 5 2 4 3.5 Surface Area =base +lateral = 10 + 27 = 37 Ratio of sides = 2:1 7 Ratio of surface areas:= 148:37 = 4:1 = 2 2 : 1 2 Example 1C: Similarity Ratios

14. Similar Solids and Volume Ratios 12.7 Similar Solids If two similar solids have a scale factor of a : b, then their volumes have a ratio of a 3 : b 3. Length/Perimeter Ratios  a:b Area Ratios  a 2 : b 2 Volume Ratios  a 3 : b 3

15. Example 1D: Similar Solids and Volume Ratios 12.7 Similar Solids 9 15 6 10 Ratio of heights = 3:2 V = r 2 h =  (9 2 ) (15) = 1215 V= r 2 h = (6 2 )(10) = 360 Ratio of volumes: = 1215:360 = 27:8 = 3 3 : 2 3

16. 1. The following solids are similar. Provide the length, area and volume ratios. Lesson Quiz: Part I Length ratios (a:b) = 3:6 = 1:2 Area ratios: (a 2 :b 2 ) = 1:4 Volume ratios: (a 3 :b 3 ) = 1:8 12.7 Similar Solids

17. 2. The following solids are similar. Provide the length, area and volume ratios. Lesson Quiz: Part II Length ratios (a:b) = 12:4 = 3:1 Area ratios: (a 2 :b 2 ) = 9:1 Volume ratios: (a 3 :b 3 ) = 27:1 12.7 Similar Solids

18. 2. The following solids are similar. Provide the ratios of the length and area. Lesson Quiz: Part III Length ratios (a:b) = 3:6 = 1:2 Area ratios: (a 2 :b 2 ) = 1:4 Volume ratios: (a 3 :b 3 ) = 27:216 12.7 Similar Solids Take the cube root of the volume to get the length ratio.

19. 2. The following solids are similar. Provide the ratios of the length and area. Lesson Quiz: Part III Length ratios (a:b) = 3:5 Area ratios: (a 2 :b 2 ) = 9:25 Volume ratios: (a 3 :b 3 ) = 27:125 12.7 Similar Solids Take the cube root of the volume to get the length ratio.

20. Videos: http://www.bing.com/videos/search?q=similar+ solids+&FORM=HDRSC3#view=detail&mid=46B C3C71CB6B6AE97EA146BC3C71CB6B6AE97EA1 12.7 Similar Solids