How can you make the largest possible open box from a flat rectangular card? In this problem, squares of equal size are cut from each corner, and the sides are folded up to form a box without a lid. By changing the size of the squares, the box’s volume changes too. Explore the card, the box, and the graph to see how the dimensions are connected and to figure out which box gives the maximum volume.
Open Box Problem
Drag the black point on the card to change the value of x and see how the box changes. Can you find the size that makes the box the biggest?