Question

directions: use this information to answer parts a and b.
emily forms a closed box from a rectangular piece of cardboard by cutting along solid lines and fo ng along dashed segments. she glues the square corner flaps of side length x to he sides they overlap when they are folded. she then folds the right side of the pattern over the left side. the narrow rectangle in the center of the patt orms a side of the box. to close the lid, emily tucks the sides of the lid inside the sides of the bottom.

part a
find a polynomial function for the volume.
enter the correct equation in the box.

Explanation:

Step1: Determine the dimensions of the box

When the box is formed, the height of the box is \(x\).
The length of the box \(l=(32 - 2x)\) (since we cut out two squares of side - length \(x\) from the length of the cardboard which is \(32\) inches).
The width of the box \(w=(14 - 2x)\) (since we cut out two squares of side - length \(x\) from the width of the cardboard which is \(14\) inches).

Step2: Use the volume formula for a rectangular prism

The volume formula for a rectangular prism is \(V=l\times w\times h\).
Substitute \(l = 32-2x\), \(w = 14 - 2x\), and \(h=x\) into the formula:

$$
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$$

Answer:

\(V = 4x^{3}-92x^{2}+448x\)