SOLUTION: From each corner of a square piece of sheet metal 18 centimeters on a side, remove a small square of the side x centimeters and turn up the edges to form an open box. What should t

Question 854618: From each corner of a square piece of sheet metal 18 centimeters on a side, remove a small square of the side x centimeters and turn up the edges to form an open box. What should the dimensions of the box be to maximize the volume?
I tried drawing a picture for this problem to see if it would help me solve it but I'm still lost! Thank you for your help.

Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
Try to first draw the two-dimensional net. Deal with the VOLUME calculation later. You will start with a square.

The original square is 18 cm by 18 cm. Draw the picture and revise accordingly:
Remove a square at each corner of dimensions x by x. This means the dimensions of what will become the base of the box are (18-2x) by (18-2x).

With the square corners removed, folding up the flaps forms the box of height x. Be SURE you understand that.

WHAT IS THE VOLUME?
It is a variable according to the formula .

The x intercepts are very easy to locate. You can either use a graphing calculator to find the maximum volume; or you can, if you understand these, find the derivative of v versus x and look for the maximum v that way.

The maximum volume occurs at x=3.
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