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.”
Lesson overview
 9.1 Warmup: The Same But Different (5 minutes)
 9.2 Activity: Water Transfer (15 minutes)

9.3 Activity: Revisiting Rotation (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 9.4 Cooldown: Cylinder Strategies (5 minutes)
Learning goals:
 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.
Learning goals (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.
Standards:
 This lesson builds on the standards: CCSS.7.G.B.4MS.7.G.4CCSS.7.G.B.6MS.7.G.6CCSS.8.G.C.9MS.8.G.9MO.7.GM.A.4bMO.7.GM.B.6bMO.8.GM.C.9b
 This lesson builds towards the standard: CCSS.HSGGMD.A.1MS.GGMD.1MO.G.GMD.A.1
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.