Education
Age Range: 14-16
Duration: 0-29 mins
• Mathematics

# Water aqueduct shapes

## Calculating the cross-sectional areas of different aqueducts

In this STEM activity students will investigate different aqueduct shapes to determine which is the most efficient design.

This is one of a set of resources developed to aid the class teaching of the secondary national curriculum, particularly KS3. It has been designed to support the delivery of key topics within mathematics and engineering.

## Activity: Calculating the cross-sectional areas of different aqueducts

In this lesson, students must calculate the cross-sectional area of various aqueducts to determine which one is most effective in terms of least water lost via evaporation.

Using our Aqueduct presentation, learners will be introduced to the engineering behind aqueducts by estimating the volume of water follow through the aqueduct in one second.

Students will then calculate the cross-sectional areas of various aqueduct shapes, including rectangles and trapezoids. To do this, learners must apply their understanding trigonometry to find the missing side lengths. Alternatively, students can use this GeoGebra file to calculate the area of the trapezium.

## The engineering context

Aqueducts are constructed to carry water across gaps such as valleys or ravines. In modern engineering, the term aqueduct is used for any system of pipes, ditches, canals, tunnels, and other structures used for this purpose. Aqueducts can be used to enable water to be transported to areas where it is in short supply.

## Suggested learning outcomes

In this activity students will apply their knowledge of mathematics such as calculating the area of a rectangle and trapezium or the volume of a cuboid. They will also be able to specifically apply their knowledge of trigonometry. Finally, they’ll learn how to plot graphs using a table of values.