Task of the Week: Archway

Created during a teacher training in Erfurt, today’s Task of the Week fokuses on the topic Archway. The topic allows different questions and problems. Some weeks ago, we already presented an archway task on the weight of an archway’s stones. Today, the maximal height of an archway is focused.

Task: Archway (Task Number: 3090)

Determine the maximal height of the archway at the Krämerbrücke. Give the result in meters with two decimals.

The most elegant solution of this task is to divide the archway into a rectangle and a semi-circle.

With this hint, it is necessary to determine the point at which the semi-circle begins and the rectangle ends. With the height of the rectangle and the radius of the semi-circle (best determined through the diameter), the height of the archway results. In case the topic circle should be highlighted even more, it is possible to ask for the circumference of the archway. Here, the relation of diameter and circumference is further focused.