12 7 Similar Solids Warm Up Lesson Presentation

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

12. 7 Similar Solids 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. Perimeter Ratio 16: 80 1: 5 2. Use problem 1 to provide the length ratio. Length Ratio: 4: 20 3. Now the answer in problem 2 to provide the scale factor (unit ratio): Unit Ration: 1: 5

12. 7 Similar Solids Objectives Find and Use the scale factor of Similar Solids Use Similar Solids to solve real-life problems.

12. 7 Similar Solids Vocabulary Similar Solids

12. 7 Similar Solids Two solids of the same type with equal ratios of corresponding linear measures (such as heights or radii) are called similar solids.

12. 7 Similar Solids Similar solids NOT similar solids

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

12. 7 Similar Solids Example 1 A: Are these Solids Similar 9 12 12 8 16 6

12. 7 Similar Solids Example 1 A: Are these Solids Similar Solution: 9 12 8 16 All corresponding ratios are equal, so the figures are similar 1 2 6

12. 7 Similar Solids Example 1 B: Decide if the solids are Similar. 18 6 4 8

12. 7 Similar Solids Example 1 B: Classifying Three-Dimensional Figures Solution: 18 6 8 Corresponding ratios are not equal, so the figures are not similar 4

12. 7 Similar Solids and Ratio of Areas • 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

12. 7 Similar Solids Example 1 C: Similarity Ratios 3. 5 8 7 4 4 10 5 2 Ratio of sides = 2: 1 Surface Area = base +lateral Surface Area =base +lateral = 40 + 108 = 10 + 27 = 148 = 37 Ratio of surface areas: = 148: 37 = 4: 1 = 2 2: 1 2

12. 7 Similar Solids and Volume Ratios • 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

12. 7 Similar Solids Example 1 D: Similar Solids and Volume Ratios 9 6 15 10 Ratio of heights = 3: 2 V = r 2 h = (92) (15) = 1215 V= r 2 h = (62)(10) = 360 Ratio of volumes: = 1215: 360 = 27: 8 = 3 3: 2 3

12. 7 Similar Solids Lesson Quiz: Part I 1. The following solids are similar. Provide the length, area and volume ratios. 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 Lesson Quiz: Part II 2. The following solids are similar. Provide the length, area and volume ratios. 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 Lesson Quiz: Part III 2. The following solids are similar. Provide the ratios of the length and area. Volume ratios: (a 3: b 3) = 27: 216 Length ratios (a: b) = 3: 6 = 1: 2 Area ratios: (a 2: b 2) = 1: 4 Take the cube root of the volume to get the length ratio.

12. 7 Similar Solids Lesson Quiz: Part III 2. The following solids are similar. Provide the ratios of the length and area. Volume ratios: (a 3: b 3) = 27: 125 Length ratios (a: b) = 3: 5 Area ratios: (a 2: b 2) = 9: 25 Take the cube root of the volume to get the length ratio.

12. 7 Similar Solids Videos: http: //www. bing. com/videos/search? q=similar+ solids+&FORM=HDRSC 3#view=detail&mid=46 B C 3 C 71 CB 6 B 6 AE 97 EA 146 BC 3 C 71 CB 6 B 6 AE 97 EA 1