Canalysis
What's the ideal size for a soda can?
Students will
- Calculate surface area and volume for different cylinders
- For a fixed volume, explore how surface area varies with the shape of a can and relate this to cost
- For a fixed volume, build a function for the surface area of a cylinder in terms of its radius
- Use technology to find the radius that minimizes surface area of a cylinder for a given volume
- Discuss why soda cans might be shaped the way they are
Before you begin
Students should know the formulas for the volume and surface area of a cylinder (or be able to derive them). It’s also important for them to know how to solve for one variable in an equation in terms of another — for example, given the formula for the volume of a cylinder, they should be able to solve for the height of the cylinder in terms of the volume and the radius. This lesson also serves as a nice application of rational functions, so it helps if students have seen these types of functions before and are able to graph them using technology.Common Core Standards
Content Standards
Mathematical Practices
Downloads
Additional Materials
- Rulers
Shoutouts
Coca-Cola
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