# Task of the Week: El volumen KIO

Our new Task of the Week was created by Angelica Benito Sualdea and Alvaro Benito Nolla de Celis in Madrid. In the following they will answer us some questions about their task “El volumen KIO” [engl. volume of one KIO tower].

*How do you get in contact with MathCityMap? *

We’ve been interested in Math Trails as an educational tool for the last recent years, and we discover MathCityMap during a talk in a conference. We really liked the idea and we immediately started to think in uploading some of our trails we had already created into the platform. It took us some time, but we finally did!

*Please describe your task. Where is it placed? What´s the topic of the task? *

The task is placed in a characteristic square in the north of Madrid. The square is dominated by two twin towers (the Puerta de Europa Towers, commonly known as the KIO Towers) which are oblique prisms bending one to each other with an angle of 14 degrees of inclination. Since 1996, they symbolise a picturesque “entrance” to the city. From a close look it realised that the towers are surrounded by a rectangular lattice, which divides each tower in a web of black aluminium windows.

Our task asks after the total volume of one of the KIO towers. It provides information about the dimensions of one of the windows: 1.20m x 1.34m. Since its volume is the same as the volume of a straight tower with the same base, to solve the task it is only needed to calculate the number of windows covering the base and the number of windows covering the height of the tower. By counting carefully, it can be checked that there are 30 windows along the base of the tower and 86 from the ground to the top, which implies that

*Vol(KIO Tower) = A*h = (30*1.20)^2*(86*1.34) = 149.351 m^3*

*Which didactic aims do you want to stimulate through this task?*

We would like to stimulate student’s ability of solving a complex problem (in this case, calculating the volume of a skyscraper) by just knowing the information of a small element of it (the dimensions of a window of the tower). We find very useful to teach that reducing problems to simpler ones is a powerful mathematical tool. Also, since the tower is an oblique prism, it’s volume is the same as the corresponding right prism, and this task is a stimulating real life example.

*Do you have any other commentary on MathCityMap?*

We love the app! we will continue creating trails and encourage our students to experience and design new trails.

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