Calculus - box problem

[Snicho1]

Hey, so ive recently started a Summer School course in Calculus, which I previously failed last year. I didnt take maths in high school, so I have no background on calculus what so ever.

I have a problem question, ive tried to attempt it by cutting out a piece of paper and attempting it visually, but im not sure how to do the guestion, i think ive got the height as x, the breadth and width as 2x and 3x. But heres the question so you know what Im talking about. Any pointers on the question would be greatly appreciated!

An open box is made from a rectangular piece of tin 10m by 8m by cutting
square pieces from each corner and folding up the sides. Each square has side length x.
Draw a diagram of the box, labeling its height, breadth and width in terms of x and what value of x produces the maximum volume of the box?

Thank you!

 

[soroban]

Hello, Snicho1!

I didn't take maths in high school, so I have no background on calculus whatsoever.
. . THERE is your problem!

An open box is made from a rectangular piece of tin 10m by 8m
by cutting square pieces from each corner and folding up the sides.
Each square has side length x.
Draw a diagram of the box, labeling its height, breadth and width in terms of x.
What value of x produces the maximum volume of the box?

The 10-by-8 sheet of tin looks like this:

      : - - -  8  - - - :
    - *---*---------*---* - 
    : |///|         |///| x
    : *---* - - - - *---* -
    : |   :         :   | :
    : |   :         :   | :
    : |   :         :   | :
   10 |   :         :   |10-2x
    : |   :         :   | :
    : |   :         :   | :
    : |   :         :   | :
    : *---* - - - - *---* - 
    : |///|         |///| x
    - *---*---------*---* -
      : x :   8-2x  : x :

x-by-x squares are removed from each corner.
. . and the sides are folded upward.


The resulting open-top box looks like this:

 [SIZE=2]         *-----------*
         /|          /| x
        / * - - - - / *[/SIZE]
[SIZE=2]       / /         / /
      *-----------* / 8-2x
    x |           |/
      *-----------*
           10-2x[/SIZE]

The volume of the box is: .\(\displaystyle V \;=\;x(8-2x)(10-2x)\)

And that is the function you must maximize.

 

[Snicho1]

Hey, thanks so much! This really helps so much!

Haha and yep, definitely an issue that I have no background, but sadly I have no other choice but to do this subject! Im trying very hard though!

Thanks a bunch! Should be able to find the next part of the question now