Minimising waste

Using energy and materials responsibly is an important aspect of designing

Manufacturers will lose money if too much scrap raw material is produced during cutting. Profits could be increased if they are able to find ways to lower the cost per product by saving material. Some manufacturers will pass on the savings that they make to the consumer and lower the cost of the product.

Tessellating shapes can help arrange items to be cut so that, when fitted together, as many as possible can be cut out of a sheet of material.

A tessellation pattern of pink and black lizards on a red background.
Tessellated shapes

Nesting software will automatically fit irregular shapes as close together as possible. A designer could use a computer aided design (CAD) package with built-in nesting tools to try different nested shapes and work out what outputs use the least surface area of material.

Example of nested shapes output by a CAD package nesting tool.Example of nesting

Lay plans are used when cutting fabrics, as fabric has a nap. This means that it has a different appearance when viewed in another direction, and that pattern pieces cannot be tessellated or nested as effectively as wood, metal or plastic.

Calculating surface area and volume

Calculating the amount of material needed can be done by using a working drawing or by measuring a prototype. Simple measurements can be used to work out the area and volume of shapes. This will help to calculate how much raw material is needed to make a product, as well as how much space would be available inside the product.

Example

Calculate the surface area of all the sides below, to determine how much timber would be needed to manufacture the jewellery box, and the volume of the finished product. In this example, include the lid in the calculation of each face.

Jewellery box with surface measurements to help calculate surface area and volume of finished product.

Surface area can be calculated by adding together the areas of the six faces.

First, find the total area of the two different-sized faces:

End panels:

End panel of jewellery measurement of 30 cm x 30 cm x 2 to help calculate surface area of jewellery box.

Area = 30 cm × 30 cm = 900 cm2

Total area = 2 × 900 cm2

= 1,800 cm2

Side panels:

Side panel measurement 60 cm x 30 cm x 4 of jewellery box to help calculate surface area of jewellery box.

Area = 60 cm × 30 cm = 1,800 cm2

Total area = 4 × 1,800 cm2

= 7,200 cm2

Surface area = 1,800 cm2 + 7,200 cm2

= 9,000 cm2

Therefore, 9,000 cm2 of timber is required to construct the jewellery box.

curriculum-key-fact
Volume of a prism = area of the cross section × length.

= 900 cm2 × 60 cm

= 54,000 cm3

Question

Calculate how much timber would be needed to manufacture the toy box below, and the volume of the finished product. Again, include the lid in your surface area calculations.

Toy box with measurements of  100 cm height x 100 cm width x 400 cm length to help calculate surface area and volume.

100 cm = 1m

Area of end panel = 1 m × 1 m = 1 m2

Total area of two end panels = 2 × 1 m2 = 2 m2

Area of side panel = 1 m × 4 m = 4 m2

Total area of four side panels = 4 × 4 m2 = 16 m2

Surface area = 2 m2 + 16 m2 = 18 m2 of timber

Volume = 2 m2 × 4 m = 8 m3