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Mathematics > Course Model Advanced Quantitative Reasoning (Advanced Course) > Geometric Measurement and Dimension
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Mathematics | Course : Model Advanced Quantitative Reasoning (Advanced Course)

Domain - Geometric Measurement and Dimension

Cluster - Explain volume formulas and use them to solve problems.

[AQR.G-GMD.A.2] - (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Resources:


  • Cavalieri's Principle
    A method, with formula given below, of finding the volume of any solid for which cross-sections by parallel planes have equal areas. This includes, but is not limited to, cylinders and prisms. Formula: Volume = Bh, where B is the area of a cross-section and h is the height of the solid.

Predecessor Standards:

  • 8.G.C.9
    Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • GEO.G-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.
  • MII.G-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.
  • MII.G-GMD.A.3
    Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*