Lesson 9
Cylinder Volumes
Lesson Narrative
In previous grades, students learned formulas for the volumes of cones, cylinders, and spheres. In this lesson, they recall how to calculate the volume of a cylinder, using informal arguments to compare the volume of a cylinder to the volume of a prism that has an equal height and area of its base. Students start to think about volume in 1unit layers. This lays a foundation for the informal derivation of the pyramid formula, which will rely on consideration of area of cross sections. Finally, students apply cylinder volume calculations to a solid of rotation.
Students have opportunities to reason abstractly and quantitatively (MP2) when they compare prism and cylinder volumes.
If necessary here and in the remainder of the unit, provide students with formulas for the areas of triangles, parallelograms, and circles. Students developed and worked with these formulas in earlier grades. Note that we use “area of a circle” as shorthand for “the area of the region enclosed by a circle.”
Learning Goals
Teacher Facing
 Explain (orally and in writing) connections between ways of finding volumes of prisms and cylinders.
 Use the cylinder volume formula to calculate volumes of composite figures and solids of rotation.
Student Facing
 Let’s analyze cylinder volumes.
Learning Targets
Student Facing
 I can calculate volumes of solids that are composed of cylinders.
 I can explain how finding the volume of a prism relates to finding the volume of a cylinder.
CCSS Standards
Building On
Addressing
Building Towards
Print Formatted Materials
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