Tin Can Design

Tin cans come in a variety of shapes and sizes. In this activity students consider the net of a tin can, the formula for the total surface area and the formula for the volume of the can. The first problem requires students to express the total surface area as a function of r by eliminating h. The second problem requires students to draw a graph of the function which requires consideration of what happens to the value of the surface area when the radius of the can equals zero and as the radius tends to infinity. The third problem requires students to find the value of r for which the surface area is a minimum. This can be achieved in a variety of ways including the introduction of calculus. Students are asked to investigate whether, in real-life, minimising the surface area is a key factor when designing cans.