Question

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 :)

Answer 1

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:

$V = A_bh$

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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 $\frac{4.5}{3} = \frac{3}{2} = 1.5$, thus, for the fourth box, the edge length, in inches, will be of $4.5 \times 1.5 = 6.75$

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• Square base, of length 6.75 inches, thus:

$A_b = 6.75^2 = 45.5625$

• Height of 9 inches, thus $h = 9$ and:

$V = A_bh = 45.5625(9) = 410.1$

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

A similar problem is given at brainly.com/question/23756783