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
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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.
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.
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