SOLUTION: The exact problem as it shows up on my homework is: An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares f

Algebra ->  Surface-area -> SOLUTION: The exact problem as it shows up on my homework is: An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares f      Log On


   

Question 701093: The exact problem as it shows up on my homework is:
An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides. What is the maximum volume of the box?
I am in an algebra 2 class, and I don't recognize any way to solve this problem using what we've learned this semester so I'm completely lost as how to solve it.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An open box of maximum volume is to be made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides. What is the maximum volume of the box?
-----
Sketch a square on a piece of paper.
Labe each side "24" cm
------
Sketch a square at each corner of the 24x24 square.
Label the sides of the little square "x"
--------
Imagine (or actually) cutting out the four x by x squares
----
Imagine (or actually) folding up the remaining sides of the sheet.
----
Find the volume of this paper box.
---
Volume = length*width*height
Volume = (24-2x)(24-2x)x
----
Can you determine the maximum volume?
Cheers,
Stan H.
===================
Cheers,
Stan H.