(a)
Explain why
The volume of the solid is difference of volume of cube of side length
Given:
Calculation:
In the given picture a cube of side length
Therefore, the volume of the solid is difference of volume of cube of side length a to the volume of cube of side length b.
And this solid is formed by combing solids of I, II, and III.
The volume of a cube is given by
Therefore, we can conclude that the sum of volumes of solid I, solid II, and solid III is given by
(b)
Write an expression for the volume of each of the three solids. Leave your expression in factored form.
Volume of solid I is given by
Volume of solid II is given by
Volume of solid III is given by
Given:
Calculation:
From the given figure,
Volume of solid I is given by
Volume of solid II is given by
Volume of solid III is given by
(c)
Derive the factoring pattern for
Given:
Volume of solid I is given by
Volume of solid II is given by
Volume of solid III is given by
Calculation:
From the given figure,
Volume of solid I is given by
Volume of solid II is given by
Volume of solid III is given by
And the sum of volume of solids I, II, and III is
Therefore,
Factored out the GCF
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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