Find the box tops!

Geometry Level 2
  • Anna has one really large box with dimensions 50 in x 30 in x 20 in made of paper without a top/lid.
  • For some reason, she decides that she wants many smaller rectangular prisms with the very specific dimensions 1 in x 2 in x 3 in, so she cuts up the big box into many smaller pieces, and uses them to make as many new boxes as she can.
  • All of these small boxes also are missing tops.

What is the maximum number of small boxes she can make?

Details and assumptions:

  • I intentionally left out the size of the top of the big box! Given the three possibilities, you can assume that the lid's size allows for the maximum number of small boxes to be formed.
  • I also left out the size of the top of the small box, so also figure out which size of a small box's lid will allow for the maximum number of small boxes.
  • Assume she cuts up the pieces and tapes them together to make new boxes. No overlapping of pieces.
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