# Task of the week: Volume of the bottle

The task of the week is back! Today we present you a task, which was developed during a teacher training at the Georg-Büchner-Gymnasium in Bad Vilbel near Frankfurt.

Next to the schoolyard we found this interesting sculpture of a water bottle. Immediately we wanted to ascertain, how many litres of water the bottle would contain. For the task “Volume of the bottle” we assume that the artwork has a wall thickness of 3 cm.

*How the volume of the bottle can be ascertained?*

For the modelling we divide the artwork in a frustum of a cone and a circular cylinder. We look on the object as compounded solid.

*What´s the aim of the task?*

The complexity of the task is to find a useful mathematic model for the object, which is a fitting transfer of the reality and is calculable with a manageable time exposure all at once. To solve the problem, you have to find a compromise between mathematical precision and practicability. Hence the task is a good example for a lot of modelling problems.

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