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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

1. Tangent Lines

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Exercise 38 Page 769

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

27:64 or 27/64

Practice makes perfect

Similar solids have the same shape and all of their corresponding dimensions are proportional. The ratio of the corresponding linear dimensions of the similar solids is the scale factor. If the scale factor of two similar solids is a:b, then the ratio of their corresponding volumes is a^3:b^3. Consider the given solids.

To find the scale factor, we will find the ratio of the heights.

a/b=6/8

a/b=.a /2./.b /2.

a/b=3/4

\dfrac a b = a:b

a:b = 3:4

The scale factor of the given cubes is 3:4. Let's now find the ratio of volumes by raising the scale factor to the third power.

a/b=3/4

LHS^3=RHS^3

(a/b)^3 = (3/4)^3

(a/b)^m=a^m/b^m

a^3/b^3 = 3^3/4^3

Calculate power

a^3/b^3 = 27/64

\dfrac a b = a:b

a^3:b^3 = 27:64

The ratio of volumes is 27:64.

Subchapter links

Lesson Check p.766

Standardized Test Prep p.769

Mixed Review p.769