Lesson plan

10. Find volumes of complex shapes involving cylinders, cones, and spheres (A)

teaches Common Core State Standards CCSS.Math.Content.8.G.C.9 http://corestandards.org/Math/Content/8/G/C/9
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2
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Lesson objective: Solve problems that involve complex shapes composed of cylinders, cones or spheres.

This lesson provides an opportunity for students to apply their knowledge and understanding of finding volumes of cylinders, cones, or spheres to a real-life situation. Students are asked to find and compare the volumes of a truncated cone-shaped container and a shape composed of a cone and a hemisphere.

Key Concepts students will use: 

  • The volume of a cone takes into account the area of the base and the height of the cylinder it "sits inside of."

  • The volume of a sphere is related to the volume of a cylinder the sphere "sits inside of."

Skills students will use:

  • Understand that volumes are additive. (Grade 5, Unit 9; 5.MD.C.5.C)
  • Find the volume of cones.
  • Find the volume of spheres.

Students engage in Mathematical Practice 2 (Reason abstractively and quantitatively) as they determine what information is given in the real-world context, modify dimensions as needed, utilize those values along with the appropriate formula to find the appropriate volumes and as they make sense of their answer within the context of the problem.

Key vocabulary: 

  • complex shape
  • cone
  • diameter
  • hemisphere
  • radius
  • volume