The Volume Formula of a Pyramid and Cone

Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from previous lessons to verify the formula and to show that it works for the general cone. 

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CCSS: Designed
Instructional Ideas

  • To remind the class of the formula for a pyramid or cone, use the the demonstration that shows it takes three cones of water to fill a cylinder with the same base and height
Classroom Considerations

  • The hands-on section in the opening requires the use of six congruent pyramids for each group or individual
  • The purpose of the lesson is not what the formula is but why the formula has a one-third
  • The eleventh installment in a 14-part series
Pros

  • Exercises require the application of the volume formula
  • Includes scaffolding suggestions for dividing the class into small groups for discussions
Cons

  • None