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Problem

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Textbook Expert
Textbook ExpertVerified Tutor
20 Nov 2021

Given information

Consider the following scenario: A box with an open top is to be made from a 3 ft wide square piece of cardboard by cutting a square from each of the four corners and bending up the edges. Determine the maximum volume that such a box can have. Obtain an equation that relates the variables of volume. 

To determine and compare the answer.

Step-by-step explanation

Step 1.

A square piece of cardboard 3 ft-wide, by cutting out a square from each corner. 

The volume (V) of the box is:

  

  

The length of the box is given as: 3 ft

The side of the box is constructed from the original square piece.

This means that:

 

So

 

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