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Mathematics > Course Model Geometry (Traditional Pathway) > Geometric Measurement and Dimension
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Mathematics | Course : Model Geometry (Traditional Pathway)

Domain - Geometric Measurement and Dimension

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

[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.

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:

  • 6.G.A.2
    Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
  • 7.G.B.4
    Circles and measurement
  • 7.G.B.4.a
    Know that a circle is a two-dimensional shape created by connecting all of the points equidistant from a fixed point called the center of the circle.
  • 7.G.B.4.b
    Understand and describe the relationships among the radius, diameter, circumference and circumference of a circle.
  • 7.G.B.4.c
    Understand and describe the relationship among the radius, diameter, and area of a circle.
  • 7.G.B.4.d
    Know the formulas for the area and circumference of a circle and use them to solve problems.
  • 7.G.B.4.e
    Give an informal derivation of the relationship between the circumference and area of a circle.
  • 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.3
    Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
  • PC.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.
  • 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.