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

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12-7Similar SolidsHolt GeometryWarm UpLesson PresentationLesson Quiz

Warm UpClassify 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 16:80Length Ratio: 4:20Unit Ration: 1:512.7 Similar Solids 1:5

Find and Use the scale factor of Similar Solids

Use Similar Solids to solve real-life problems.Objectives12.7 Similar Solids

Similar Solids

Vocabulary12.7 Similar Solids

12.7 Similar SolidsSimilar SolidsTwo solids of the same type with equal ratios of corresponding linear measures (such as heights or radii) are called similar solids.

12.7 Similar SolidsSimilar solidsNOT similar solids

12.7 Similar SolidsSimilar Solids & Corresponding Linear MeasuresLength: 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

Example 1A: Are these Solids Similar12.7 Similar Solids

Example 1A: Are these Solids Similar12.7 Similar SolidsAll corresponding ratios are equal, so the figures are similar Solution:

Example 1B: Decide if the solids are Similar.12.7 Similar Solids

Example 1B: Classifying Three-Dimensional Figures12.7 Similar SolidsCorresponding ratios are not equal, so the figures are not similarSolution:

12.7 Similar SolidsIf two similar solids have a scale factor of a : b, then corresponding areas have a ratio of a2: b2.

This applies to lateral area, surface area, or base area.

Length/Perimeter ratio a:bArea Ratios a2 : b 2 Similar Solids and Ratio of Areas

12.7 Similar Solids1048Surface Area = base +lateral = 40 + 108 = 148Surface Area =base +lateral = 10 + 27 = 37Ratio of sides = 2:1Ratio of surface areas:= 148:37 = 4:1 = 22: 12Example 1C: Similarity Ratios

Similar Solids and Volume Ratios 12.7 Similar SolidsIf two similar solids have a scale factor of a : b, then their volumes have a ratio of a3 : b3.Length/Perimeter Ratios a:bArea Ratios a2: b2Volume Ratios a3: b3

Example 1D: Similar Solids and Volume Ratios 12.7 Similar SolidsRatio of heights = 3:2V = r2h = (92) (15) = 1215 V= r2h = (62)(10) = 360Ratio of volumes: = 1215:360 = 27:8 = 33: 23

1. The following solids are similar. Provide the length, area and volume ratios.

Lesson Quiz: Part ILength ratios (a:b) = 3:6 = 1:2Area ratios: (a2:b2) = 1:4

Volume ratios: (a3:b3) = 1:8

12.7 Similar Solids

2. The following solids are similar. Provide the length, area and volume ratios.

Lesson Quiz: Part IILength ratios (a:b) = 12:4 = 3:1 Area ratios: (a2:b2) = 9:1 Volume ratios: (a3:b3) = 27:1

12.7 Similar Solids

2. The following solids are similar. Provide the ratios of the length and area.

Lesson Quiz: Part IIILength ratios (a:b) = 3:6 = 1:2 Area ratios: (a2:b2) = 1:4 Volume ratios: (a3:b3) = 27:216 12.7 Similar SolidsTake the cube root of the volume to get the length ratio.

2. The following solids are similar. Provide the ratios of the length and area.

Lesson Quiz: Part IIILength ratios (a:b) = 3:5 Area ratios: (a2:b2) = 9:25 Volume ratios: (a3:b3) = 27:12512.7 Similar SolidsTake the cube root of the volume to get the length ratio.

Videos: http://www.bing.com/videos/search?q=similar+solids+&FORM=HDRSC3#view=detail&mid=46BC3C71CB6B6AE97EA146BC3C71CB6B6AE97EA112.7 Similar Solids

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