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?

Solution Preview

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.

A square sheet of cardboard 24 inches on a side is made into a box by cutting squares of equal size from each corner of the sheet and folding the projecting flaps into an open top box. What should be the length of the edge of any of the cutout squares to give thebox maximum volume?
4 inches
4.5 inches

A square sheet of cardboard 24 inches on a side is made into a box by cutting squares of equal size from each corner of the sheet and folding the projecting flaps into an open-topbox. What should be the length of the edge of any of the cutout squares to give thebox maximum volume?
4 inches
4.5 inch

An open-topbox 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 thevolume of thebox in terms of x.
b) Graph this function and

You are planning to make an open rectangular box from a 12-by 14-cm piece of cardboard by cutting congruent squares from the corners and folding up the sides.
a) What are the dimensions of thebox of larges volume you can make this way?
b) What is its volume?

1.You are to design a container box by cutting out the four corners of a square cardboard sheet that is 1600 cm2 in area. Thebox must have a square base and an open top. Determine the dimensions of thebox that give maximum volume.
2.Sketch the graph of the function f(x)=x2+4 Identify the following features of the graph:

A box is made from a sheet of metal that is 8 meters by 10 meters, by removing a square from each corner of the sheet and folding up the sides. Find the width of the square to removed in order to have a box of maximum volume.

An open-topbox is to be constructed from a 6 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. Find the function V that represents thevolume of thebox in terms of x.

An open-topbox is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x donate the length of each side of the square to be cut out. find the function V that represents thevolume of thebox in terms of x.