Students understand the precise language that describes the properties of volume. Students understand that the volume of any right cylinder is given by the formula area of base×height.

Teacher and Student versions of full lesson from engageNY

Students use Cavalieri’s principle and the cone cross section theorem to show that a general pyramid or cone has volume (1/3)Bh where B is the area of the base and h is the height by comparing it with a right rectangular pyramid with base area B and height h.

Teacher and Student versions of full lesson from engageNY

Students give an informal argument using Cavalieri’s principle for the volume formula of a sphere and use the volume formula to derive a formula for the surface area of a sphere.

Teacher and Student versions of full lesson from engageNY