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Maximizing the Volume of an Open-Top Box

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An open top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out.

Find the function V that represents the volume of the box in terms of x. Show and explain the answer, and also graph this function.

Using the graph what is the value of x that will produce the maximum volume?

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https://brainmass.com/math/geometry-and-topology/77030

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After cutting four squares, the length that is left is 8-2x feet and the width that is ...

Solution Summary

This solution provides a detailed response, which illustrates how to calculate the volume of an open-top box. The solution is easy to follow and includes a graph, which is attached in an accompanying Word document as part of this solution.

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Maximizing the Volume of an Open Top Box by Graphing

An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
a) Find the function V that represents the volume of the box in terms of x.
b) Graph this function and show the graph over the valid range of the variable x..

Using the graph, what is the value of x that will produce the maximum volume?

2. The volume of a cylinder (think about the volume of a can) is given by V = pi r^2 h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.
a) Write h as a function of r. Keep "pi" in the function's equation

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