Post on 28-Dec-2015
12.7 Similar Solids
Definitions of Similar Solids
Similar Solids have congruent angles and linear measure in the same ratios.
99
9
33
3
Scale factor 9 : 3Perimeter of the base is 9(4) and 3(4)
Ratio of the Bases 36 : 12Same as the Scale Factor 9:3
Definitions of Similar Solids
If the Scale Factor is 9:3,
Then the S.A. ratio is 92:32 or 81:9
99
9
33
3
Scale factor 9 : 3Perimeter of the base is 9(4) and 3(4)
Ratio of the Bases 36 : 12Same as the Scale Factor 9:3
Definitions of Similar Solids
If the Scale Factor is 9:3,
Then the Volume ratio is 93:33 or 729:27
99
9
33
3
Scale factor 9 : 3Perimeter of the base is 9(4) and 3(4)
Ratio of the Bases 36 : 12Same as the Scale Factor 9:3
How to remember the ratios
If the Scale Factor is a : b
the Perimeter ratio is a :b, since it in one dimension
the Surface Area ratio is a2:b22,, since it in two dimensions.
The Volume ratio is a3:b3, since it in three dimensions.
Two rectangular prisms are similar
The Scale Factor of the Prisms (A:B) are to
1:4
If the Surface Area of Prisms A is 28m2 and its Volume is 8m3
Find the Surface Area and Volume
of Prisms B
Two rectangular prisms are similar
The Scale Factor of the Prisms (A:B) are to
1:4
If the Surface Area of Prisms A is 28m2 and its Volume is 8m3
Find the Surface Area and Volume
of Prisms B
64
1
16
1
4
1RatioVolumeandRatioAreafactorScale
Two rectangular prisms are similar
If the Surface Area of Prisms A is 28m2 and its Volume is 8m3
64
1
16
1
4
1RatioVolumeandRatioAreafactorScale
2448..448
1162816
128
..
..
mBofASx
xxBofAS
AofAS
Two rectangular prisms are similar
If the Surface Area of Prisms A is 28m2 and its Volume is 8m3
64
1
16
1
4
1RatioVolumeandRatioAreafactorScale
3512.512
164864
18
mBofVx
xxBofV
AofV
Two similar cubes have volumes 64in3 and 1000in3
Find the scale factor
5
2
10
4
1000
64
1000
643
3
Homework
Page 769 – 771
# 10 – 24, 28, 29