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Coca-Cola is one of the biggest companies in the world. It’s also one of the most successful, raking in billions of dollars every year. But is it overlooking a cost-saving opportunity in something as basic as the design of its classic can?

In this lesson, students will use surface area and volume to model the cost of a soda can. Then, they’ll come up with a rational function to search for a can design that’s even less expensive to make than the current one.

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

Additional Materials

  • Rulers