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