Suppose cardboard for your product comes in ( 16 ) x ( 10 ) sheets. You want to construct a box (ignore the top) that will hold the most of your product. To construct a rectangular prism from the sheet, you cut out congruent squares from the corners, and then fold up the sides
Part 1:
Cut 1 by 1 inch squares from each corner.Fold up the sides to form the open box.
What are the dimensions of the box?
(10-2),(16-2),1
What is its volume?
V=width*length*hight
V=14*8*1
Part 2:
Use another paper of same measurement and repeat the step 1 above using different square dimension to cut from each corner and then fill in this table.
Part 3:
what is the maximum size of square that can be cut away?
Part 4:
How large should the squares be to make the box hold as much as possible? What is the resulting volume?
One size of square that will yield a box with the maximum possible volume. You can find this value by setting up and solving a simple derivative calculus problem