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Volume of a Box made from a piece of paper

Four equally sized squares are cut from the corners of an 8.5 x 11 piece of paper, and the resulting flaps are folded up to form a box. What size square will make the box of largest possible volume?
  • First drag the slider back and forth to see the squares change size.
  • Then click the checkbox for ShowBox to see the resulting box. Again drag the slider back and forth. What side length appears to give the largest volume?
  • Finally, click the checkbox for ShowGraph to see a graph of Volume versus side length. Use this graph to estimate the side length that gives the greatest volume? How close were you in your previous guess?