Differentiation

[completeheart]

Problem: A steel fabricator wants to create open-topped storage boxes out of steel with the
maximum possible volume. He can obtain square sheets of steel that have a side of 15m. He will
make the boxes by cutting identical squares from each corner of the steel sheeting and folding
the “sides” of the box. What size of small squares will give the maximum possible volume?
What will this volume be?


Please help me, my whole class is confused with this project. we only have a diagram.
Thanking you in advance

 

[Deleted member 4993]

Problem: A steel fabricator wants to create open-topped storage boxes out of steel with the
maximum possible volume. He can obtain square sheets of steel that have a side of 15m. He will
make the boxes by cutting identical squares from each corner of the steel sheeting and folding
the “sides” of the box. What size of small squares will give the maximum possible volume?
What will this volume be?


Please help me, my whole class is confused with this project. we only have a diagram.
Thanking you in advance

After cutting the corner squares (of side 'x'), what should the steel piece look like (like a cross).

Do you see how a box can be made by "folding up" the arms of the cross?

Draw a picture and put dimensions. Tell us what you found.

This is a relatively easy project - I am not sure why you are confused.

Do you know the relation between "maximum" and a derivative?

 

[JeffM]

I’ll give a hint

[MATH]V = f(x) = \text {WHAT?}[/MATH]
where V equals the volume of the box and x equals the variable defined by Subhotosh Khan.

 

[HallsofIvy]

If your plates are initially 15 m on a side and you cut squares of x m from each corner, you have a central square 15-2x meters on a side with four "wings", that will be folded up that are 15- 2x meters on one side and x meters on the other.