Math Playground
Activities

Soup Can

Same volume, less metal — what shape minimises the can?

Manufacturers want minimum metal for maximum soup. For a fixed volume, what shape uses the least material?

Optimal can
h = 2r

Height equals diameter. Calculus says this minimises surface area for a given volume.

Real cans are usually taller than 2r — because labels and stacking matter too. Maths gives the optimum; reality compromises.