Task of the Week: Water in the Fountain

A popular MathCityMap task is concerned with the volume of fountains and how many liters of water are contained. The question can be used for a wide range of geometric themes, depending on the shape of the selected fountain (rectangular, circular, …). The Task of the Week is a particular challenge because the fountain has to be modeled with help of different geometric bodies.

Task: Water in the Fountain (task number: 1420)

How many liters of water are in the illustrated fountain?

The illustrated fountain can be modeled using a cuboid and a cylinder (divided into two parts). If this has been recognized, the necessary quantities must be collected and the individual volumes calculated. Finally, the conversion in liters is required. The task with cylinders can be used from class 9 onwards; simpler fountain shapes are already possible from class 6 onwards.

Depending on the structure of the well, the collection of the data can be a challenge and the students have to become creative. For example, the circumference of a circle can be helpful for the determination of the diameter. Not at least through such considerations, a flexible handling of mathematical formulas and correlations is promoted.