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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

7. Areas and Volumes of Similar Solids

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Exercise 35 Page 748

Given the scale factor, we square it to get the surface area ratio. Follow a similar idea for the volume ratio.

Similarity Ratio	Ratio of Surface Areas	Ratio of Volumes
3:5	9:25	27:125

Practice makes perfect

Two similar solids have a scale factor ratio of 3:5. 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

a= 3 and b= 5

3^2/5^2

Calculate power

9/25

\dfrac a b = a:b

9 : 25

The ratio of their surface areas is 925 and can also be written as 9:25.

Ratio of Volumes

Let's use the Areas and Volumes of Similar Solids Theorem again to recall 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

a= 3 and b= 5

3^3/5^3

Calculate power

27/125

\dfrac a b = a:b

27 : 125

The ratio of their volumes is 27125 and can also be written as 27:125.

Similarity Ratio	Ratio of Surface Areas	Ratio of Volumes
3:5	9:25	27:125

Subchapter links

Lesson Check p.745

Practice and Problem-Solving Exercises p.746-749

Standardized Test Prep p.749

Mixed Review p.749