MA19.8.29

Mathematics (2019) Grade(s): 8

MA19.8.29

Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions.

Unpacked Content

Knowledge

Students know:
  • The volume formulas for cylinders, cones, and spheres.
  • That 3.14 is an approximation of pi commonly used in these volume formulas.
  • That composite three dimensional objects in the real world can be created by combining cylinders, cones, and spheres in part or whole.

Skills

Students are able to:
  • Calculate the volume of cones, cylinders, and spheres given in real-world contexts. often times approximating solutions to a specified decimal place.
  • Identify the components of a composite figure as being portions of or whole cylinders, cones, and spheres.
  • Combine the results of calculations to find volume for real-world composite figures.

Understanding

Students understand that:
  • the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.

Vocabulary

  • Radius
  • Pi
  • Volume
  • Cylinder
  • Cone
  • Sphere
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