Task of the Week: Diogenes and his Barrel

Doing mathematics surrounded by a fantastic setting – that promises the current Task of the Week to the statue of Diogenes of Sinope. Known as an influential Greek philosopher, he is said to have no permanent home and, instead, often spent the night in a barrel. This barrel is the core of our mathematical calculations.

Task: Diogenes and his barrel (task number: 4467)

Determine the volume of the barrel in which Diogenes lives. Give the result in liters.

How can the barrel best be described by known geometric bodies? Certainly different models are possible. A sufficiently accurate model is the use of two truncated cones, with each of the bases with the larger radius in the middle of the barrel abut each other.

The height is easily determined by measuring the height of the barrel divided by 2. By means of the circumference in the middle of the barrel and at the bottom / top each, the small and large radius can be determined. Hereby, the regular patterns on the barrel can help.

Using the formula for a truncated cone then results in the approximate volume for the entire barrel.