Exercise 34 Page 748

Two similar solids have a scale factor of 1:2. We want to find the ratio of their surface areas and the ratio of their volumes.

Ratio of Surface Areas

Let's use the Areas and Volumes of Similar Solids Theorem to recall the relationship between the scale factor and area.

Areas and Volumes of Similar Solids Theorem

If the scale factor of two similar solids is ab or a:b then the ratio of their areas is a^2b^2 or a^2:b^2.

To find the ratio of their surface areas we will substitute in the scale factor values.

a^2/b^2

Substitute

a= 1 and b= 2

1^2/2^2

CalcPow

Calculate power

1/4

FracToScale

\dfrac a b = a:b

1 : 4

The ratio of their surface areas is 14, and can also be written as 1:4.

Ratio of Volumes

We can again use the Areas and Volumes of Similar Solids Theorem to find the relationship between the scale factor and volume.

Areas and Volumes of Similar Solids Theorem

If the scale factor of two similar solids is ab or a:b then the ratio of their volumes is a^3b^3 or a^3:b^3.

To find the ratio of their volumes we will substitute in the scale factor values.

a^3/b^3

Substitute

a= 1 and b= 2

1^3/2^3

CalcPow

Calculate power

1/8

FracToScale

\dfrac a b = a:b

1 : 8

The ratio of their volumes is 18, and can also be written as 1:8.

Similarity Ratio	Ratio of Surface Areas	Ratio of Volumes
1:2	1:4	1:8