SOLUTION: I'd appreciate some a detailed explanation of this problem in words, please!!! You have a flat sheet of cardboard that is 10 inches long and 8 inches wide. You need to make a bo

Question 1174928: I'd appreciate some a detailed explanation of this problem in words, please!!!
You have a flat sheet of cardboard that is 10 inches long and 8 inches wide. You need to make a box that has the maximum volume. So, you decide to cut out square corners of the sheet of cardboard and fold the cardboard to make a box. Let x represent the side of each little square you cut out. Write a function for the area of the box and use your graphing calculator.
What is the maximum area of your box, and what value of x gives you that maximum volume? Be sure to justify your
answer.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Hello, I want to answer your question/questions step by step, in all details.

(1)  The question for the maximum volume is good and is reasonable.

     The question about the maximum area is NONSENSICAL:  than lesser area of the corner squares you cut, than greater is the surface area.



(2)  THEREFORE, the correct question consists of two parts:


          a)  Find the maximum possible volume,  and

          b)  Find the surface area, corresponding to the maximum volume.



(3)  Regarding the maximum volume, you just got the solution yesterday at the link

     https://www.algebra.com/algebra/homework/Human-and-algebraic-language/Human-and-algebraic-language.faq.question.1174860.html



(4)  Another solution to this problem (finding maximum volume) you may read from my lesson

     https://www.algebra.com/algebra/homework/word/misc/Calculus-optimization-problems.lesson

     in this site  (Problem 3 in this lesson).



(5)  After finding the dimensions of the box, you can easily find the surface area making simple arithmetic.

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