Cubed Cans

In this lesson, students will use formulas they have explored for the volume of a cylinder and convert them into the same volume for rectangular prisms while trying to minimize the surface area. Various real world cylindrical objects will be measured and converted into a prism to hold the same volume. As an extension, students may design and create a rectangular prism container according to their dimensions to compare and contrast with the cylinder.

Weblink address (URL): 
Cubed Cans

Standards & Objectives

Learning objectives: 

Learning Objectives:

Students will:

  • Use and explore volume formulas for cylinder and prisms.
  • Create dimensions for a prism based on a fixed volume.
  • Solve problems using the volume formulas.
  • Explore surface areas.
Essential and guiding questions: 

Questions for Students:

  • How does the volume formula for a cylinder relate to the volume formula of a prism?
  • How can the volume of a cylinder can be determined without filling it with objects?
  • Do cylinders and cubes with the same volume have the same surface area?

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 

Extensions:

  • Have students create a cylinder based on a rectangular prism.
  • Give students 36 blocks. Students will need to create a box using the dimensions 1 × 1 × 36. Next, ask students to create other boxes from the same 36 blocks. You will want to clear up any misconceptions that 1 × 36 × 1 is a different box. It is in fact the same as the previous box, but in a different orientation. As students create the boxes, ask them to find the surface area as well. They can do these two ways. They can use the length, width, and height dimension formula or students can count the squares on each side of the box they created. This will allow for a concrete way for students to explore finding surface area and why the formula works. Once students have found all possible boxes, ask students if they see any patterns in the dimensions of the boxes and the surface areas. Lead students in discussing that as the shape of the boxes became closer to a cube, the surface area decreased. The lowest surface area we could create would be the shape that is closest to a cube.

Helpful Hints

Materials:

  • Various cylindrical cans
  • Rulers
  • Flexible tape measures (optional, if you prefer the circumference measured)
  • Calculators
  • Cubed Cans Activity Sheet 

References

Contributors: 
Roxann Johnson
Originator: 
Ayers Institute for Learning & Innovation