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Function Expressing Volume of a Cardboard Box

Please help with the following problem. Please provide step by step calculations for each.

A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 10 in. by 17 in. by cutting equal squares from the four corners and turning up the sides. (a) Find a mathematical model expressing the volume of the box as a function of the length of the side of the square cut out. (b) What is the domain of the function obtained in part (a)? (c) On a graphics calculator, find accurate to three decimal places the length of the side of the square cut out so that the box has the largest possible volume. What is the maximum volume?

Solution Preview

Length = 10
Breadth = 17
Let x inches be the side of the square that is cut off from all the four couner
Lenght becomes = ...

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The function expressing volume of a cardboard box is investigated in the following posting. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.