Chapter 12 12.7 Similar Solids Two Solids with equal ratios of corresponding linear measurements...
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Transcript of Chapter 12 12.7 Similar Solids Two Solids with equal ratios of corresponding linear measurements...
Chapter 1212.7
Similar Solids
Similar Solids• Two Solids with equal ratios of
corresponding linear measurements
18
6
8
2
8
2
Ratios Not Equal Not Similar
15
10
45
30
Ratios equal
Solids are similar
Determine if the following solids are similar if so determine the scale
factor
14
7
14
7
12
5
Ratios not equal
Solids not similar
Yes: Scale Factor = 8
5
Theorem 12.13 Similar Solids Theorem
• If two solids have a scale factor of a:b then:– Corresponding area have a ratio of a2:b2
– The corresponding volumes have a ratio of a3:b3
• Example: If two similar solids have a scale factor of 4:5, then– The ratio of their surface areas is 16:25– The ratio of their volumes is 64:125
The solid is similar to a larger solid with the given scale factor. Find the surface
area S of the larger solid
Surface Area
1. surface area ratio =4
1
2
12
2832
208
4
1
inx
x
2. Set up the proportion and solve
The solid is similar to a larger solid with the given scale factor. Find the volume
V of the larger solid
Volume
1. Volume ratio =8
1
2
13
32560
320
8
1
inx
x
2. Set up the proportion and solve
The solid is similar to a larger solid with the given scale factor. Find the surface
area S of the larger solid
Surface Area
1. surface area ratio =9
1
3
12
23582
398
9
1
inx
x
2. Set up the proportion and solve
The solid is similar to a larger solid with the given scale factor. Find the volume
V of the larger solid
Volume
1. Volume ratio = 27
1
3
13
313365
495
27
1
inx
x
2. Set up the proportion and solve
The solid is similar to a larger solid with the given scale factor. Find the surface
area S of the larger solid
Surface Area
1. surface area ratio =9
4
3
22
2
4 144
9
324
x
x cm
2. Set up the proportion and solve
The solid is similar to a larger solid with the given scale factor. Find the volume
V of the larger solid
Volume
1. Volume ratio =27
8
3
23
3
8 288
27
972
x
x cm
2. Set up the proportion and solve
The solid is similar to a larger solid with the given scale factor. Find the surface
area S of the larger solid
Surface Area
1. surface area ratio =16
9
4
32
2
9 96
16512
3
x
x cm
2. Set up the proportion and solve
The solid is similar to a larger solid with the given scale factor. Find the volume
V of the larger solid
Volume
1. Volume ratio =64
27
4
33
3
27 96
642048
9
x
x cm
2. Set up the proportion and solve
Homework #69Pg 769-772 10-24 even, 25-29