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# Mathematics in Real Life Contexts - Steel Mill

A collection of six resources exploring the mathematics used in the production of steel. Students explore the: *Design of tin cans requiring the formation of equations, calculation of the volume of a cylinder and the minimum value for surface area. *Most efficient way to stamp out the template for a drinks can from a sheet of steel requiring the calculations of areas of squares, circles and the use of trigonometry. *Elimination of wavy edges in steel production using Pythagoras' theorem, trigonometry and the calculation of the length of the arc of a sector. *Transportation costs associated with supplying goods to the correct place. *Use of repeated percentages to calculate the reduction in width of tinplate and solve problems using trial and improvement or logarithms. *Volume and weight of tinplate held on a cylindrical roll and the length of tinplate produced.

## Resources

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### 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...

### Drinks Cans

Drinks cans are made by stamping out circular discs from a sheet of tin. Given the dimensions of the sheet of tin and the diameter of the circle stamped out, students are required to calculate the wastage and to investigate whether there is a more efficient method. The problem requires students to be able to...

### Wavy Edges

Due to problems in the manufacture of tinplate coils, the edge of the strip can be slightly longer than the centre. This causes a 'wave' on the wall of the coil but can be rectified by differentially stretching the strip to make the edges flat. Students are required to apply Pythagoras' theorem to find the radius...

### Transportation

The cost of transportation is a key factor for many industries. This activity features a classic transportation problem giving the outputs of two suppliers, the demands of two consumers and the associated transportation costs. Students are asked to find the minimum transportation cost to meet the demand. Students...