Context

Prisms are geometric solids that are very present in our daily lives, whether in the form of boxes, packaging, buildings, and so on. They are three-dimensional shapes with polygonal faces and have a very interesting property: their volume is always given by the product of the area of their base by the height. But how can we calculate the area of bases of different shapes? And how can the volume of a prism help us understand or solve problems in our daily lives?

The ability to calculate volumes of prisms can become extremely useful in various situations. Imagine, for example, that you need to paint a wall in your house. The amount of paint you will need is directly related to the volume of the prism that represents the wall, considering the layer of paint as one of its dimensions. In the construction sector, volume calculations are essential to define the amount of material needed for a construction project.

Prisms are not only present in objects in our daily lives, but they are also fundamental in the study of more advanced concepts in computer graphics and physics. Therefore, understanding how to calculate the volume of prisms allows us not only to solve simple problems but also to better understand the world around us.

To deepen the studies on prisms, I suggest consulting the book 'Fundamentos de Matemática Elementar: Geometria Espacial, Métrica Plana' by Osvaldo Dolce and José Nicolau Pompeo, as well as the website 'Mundo Educação' in the section on Spatial Geometry. In addition, the videos from the channel 'Matemática Rio with Prof. Rafael Procopio' on YouTube are also a great source of learning on the subject.

• Book: Dolce, Osvaldo, and José Nicolau Pompeo. Fundamentos de Matemática Elementar: Geometria Espacial, Métrica Plana. Atual, 1993.
• Website: Mundo Educação. Geometria Espacial. Available at: https://www.mundoeducacao.uol.com.br/matematica/geometria-espacial.htm
• Video: Matemática Rio with Prof. Rafael Procopio. PRISMS: what are they? (Part 1 of 2). Available at: https://www.youtube.com/watch?v=6O2Uvwyt7UQ

Practical Activity 'Mathematics and Arts: Building and Calculating Prism Volumes'

Project Objective

The project aims to deepen knowledge about prism volumes in a playful and practical way, enabling students to perceive the applicability of this concept in daily life and its relevance in various sectors of everyday life.

Project Description

Students will be divided into groups of 3 to 5 and will be required to construct three different types of prisms (triangular prism, rectangular prism, and hexagonal prism) using recyclable materials such as cereal boxes, cardboard, or any other material available in their homes.

Each group will paint and decorate the constructed prisms, estimating the amount of paint that will be needed to paint each prism. They will then calculate the volume of each constructed prism and compare the calculated volume with the amount of paint used in the painting.

Required Materials

• Cereal boxes or cardboard;
• Ruler or tape measure;
• Scissors;
• Glue;
• Acrylic paint and brushes;
• Calculator.

Project Step by Step

1. Divide into groups of 3 to 5 students.
2. Choose the three types of prisms you intend to build.
3. Using cereal boxes or cardboard, construct each of the chosen prisms. Make the necessary measurements with the ruler or tape measure, cut the desired shapes with the help of scissors, and glue the parts together.
4. Paint and decorate the prisms in the way you find most interesting.
5. Calculate the volume of each constructed prism using the corresponding formula for each type of prism.
6. Estimate the amount of paint used in the painting of each prism and compare it with the calculated volume.
7. Record the entire process of construction, painting, and calculation of the prisms.

Project Delivery

After completing the practical part, each group must prepare a written report containing the following points:

1. Introduction: Contextualization of the theme, its relevance and application in the real world, as well as the objective of this project.
2. Development: Theory on the calculation of prism volumes, detailed description of the practical activity, methodology used, and presentation and discussion of the results obtained.
3. Conclusion: Recap of the main points of the work, lessons learned, and conclusions drawn from the project.
4. Bibliography: References to the materials consulted for the project.

In addition to the report, each group must present the constructed prisms, as well as a photographic or video record of the construction and painting process of the prisms.