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A company makes gift boxes in different sizes following the pattern shown below. What is the volume of the fourth gift box to the nearest cubic inch? - see attachment :)

A Company Makes Gift Boxes In Different Sizes Following The Pattern Shown Below What Is The Volume Of The Fourth Gift Box To The Nearest Cubic Inch See Attachme class=

Answer :

The volume of the fourth box is of 410.1 cubic inches.

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The volume of a rectangular prism is given by the base area multiplied by the height, that is:

[tex]V = A_bh[/tex]

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  • For the first three boxes, the height is constant at 9 inches.
  • At the base, the edge length is multiplied by 1.5 each time, as [tex]\frac{4.5}{3} = \frac{3}{2} = 1.5[/tex], thus, for the fourth box, the edge length, in inches, will be of [tex]4.5 \times 1.5 = 6.75[/tex]

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  • Square base, of length 6.75 inches, thus:

[tex]A_b = 6.75^2 = 45.5625[/tex]

  • Height of 9 inches, thus [tex]h = 9[/tex] and:

[tex]V = A_bh = 45.5625(9) = 410.1[/tex]

The volume of the fourth gift box will be of 410.1 cubic inches.

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