12-7 Similar Solids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson...
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Transcript of 12-7 Similar Solids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson...
12-7 Similar Solids
Holt Geometry
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson 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 16:80
Length Ratio: 4:20
Unit Ration: 1:5
12.7 Similar Solids
1:5
Find and Use the scale factor of Similar Solids
Use Similar Solids to solve real-life problems.
Objectives
12.7 Similar Solids
12.7 Similar Solids
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 & Corresponding Linear Measures
123
6
82
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
Example 1A: Are these Solids Similar
12.7 Similar Solids
16
12
8
612
9
All corresponding ratios are equal, so the figures are similar
16 4:12 38 4:6 312 4:9 3
length
width
height
Solution:
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:
8 2:4 1
radius
18 3:6 1
height
12.7 Similar Solids
• If 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:b
• Area Ratios a2 : b 2
Similar Solids and Ratio of Areas
12.7 Similar Solids
10
4
8
Surface Area = base +lateral = 40 + 108
= 148
52
4
3.5
Surface Area =base +lateral = 10 + 27
= 37
Ratio of sides = 2:1
7
Ratio of surface areas:= 148:37 = 4:1 = 22: 12
Example 1C: Similarity Ratios
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 a3 : b3.
Length/Perimeter Ratios a:b
Area Ratios a2: b2
Volume Ratios a3: b3
Example 1D: Similar Solids and Volume Ratios
12.7 Similar Solids
9
15
6
10
Ratio of heights = 3:2
V = r2h = (92) (15) = 1215
V= r2h = (62)(10) = 360
Ratio of volumes: = 1215:360 = 27:8 = 33: 23
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: (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 II
Length 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 III
Length ratios (a:b) = 3:6 = 1:2
Area ratios: (a2:b2) = 1:4
Volume ratios: (a3:b3) = 27:216
12.7 Similar Solids
Take 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 III
Length ratios (a:b) = 3:5
Area ratios: (a2:b2) = 9:25
Volume ratios: (a3:b3) = 27:125
12.7 Similar Solids
Take the cube root of the volume to get the
length ratio.
Videos:
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12.7 Similar Solids