Informal arguments for volume formulas
• Give dissection arguments that yield the volume formula for prisms. • Use the volume formula for prisms and an informal limit argument to obtain the volume formula for cylinders. • Obtain the formula for volume of a pyramid with square base via dissection.
In this unit students give more sophisticated, although still informal, arguments for the circumference, area, and volume formulas that they learned in earlier grades. These arguments rely on dissections, informal limits, and Cavalieri’s Principle. After giving arguments for the volume formulas, students use these formulas in solving a variety of modeling problems, including problems that involve density.
Tasks
1
Volume formulas for cylinders and prisms
2
Volume of a Special Pyramid