HSG.GMD.A.1, A.2

[BobT]

“CCSS.Math.Content.HSG.GMD.A.1
“Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

“CCSS.Math.Content.HSG.GMD.A.2
“(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.”

I am reviewing the CME Integrated II math text published by Pearson. The writers do implement Cavalieri’s principle to calculate the volume of a sphere. It seems quite awkward compared to Archimedes’ solution in his Method. Is there any background for the decision to use Cavalieri’s principle in the GMD Standard? Thanks for any perspectives.

[Bill McCallum]

Well, I would need to know exactly which methods you are talking about here. I don’t know which method CME uses. The argument I remember from Archimedes involves balancing the areas of different slices … this is arguably making use of Cavaleieri’s principle, whose essence is slicing. Happy to answer in more detail if you can be more explicit.

[Author]

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