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The Best Open Box: Modeling and Optimization

Cut squares from a sheet to fold an open box, then model its volume and find the cut that holds the most.

Grade 12Math ChallengeMath OlympiadBuildMathEngineeringGeometryMeasurementLogicAdvanced60 to 90 min7 materials

What you'll learn

  • Write a volume function V(x) from a geometric situation and state its domain
  • Find the maximum using a table, a graph, and a derivative
  • Compare a calculated maximum to a physical measurement

Objective

Build a physical model of an optimization problem, write the volume function, and use algebra and calculus to find the maximum.

STEM concepts

Mathematical modelingOptimizationVolumeEngineering designMeasurement error
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