Contextualization

Mathematics is a fundamental tool in our daily lives, being used in various areas such as commerce, engineering, architecture, and physics. The theme of cylinders and volume is especially important, as this geometric shape is present in many objects and structures that we use daily. From soda cans to pipes that transport water to our homes, cylinders are an essential part of our daily lives.

An incredibly useful skill to learn is how to calculate the volume of a cylinder. Volume is the amount of space occupied by an object, or in the case of a cylinder, it is the amount of space inside the cylinder. Without this calculation, it would be impossible to determine the capacity of cylindrical containers, such as barrels or gas tanks. Furthermore, it is a fundamental skill for those who wish to pursue careers in areas that involve volume calculations, such as architecture, engineering, physics, and industrial design.

Through our project, we aim to connect mathematical theory with concrete and tangible applications. This, in addition to facilitating the absorption of the content, will make learning more relevant and interesting.

To base your studies and deepen your knowledge on the subject, we suggest the following resources:

• Khan Academy: Cylinders, Spheres, and Cones
• Brasil Escola: Cylinder Volume
• Just Mathematics: Cylinders
• Brilliant Mathematics: Calculation of Cylinder Area and Volume.

These platforms contain concepts, examples, and exercises that will help you become masters in cylinders and volumes.

Practical Activity

Activity Title: "Cylinders Around the World"

Project Objective

The objective of this project is for students to apply the mathematical concept of cylinder volume in practical and everyday situations, not only understanding the theory behind the calculation but also valuing the importance of this knowledge in various real-life situations.

Project Description

Groups will be challenged to identify cylindrical objects in their homes or communities and calculate the volume of these objects. Then, the groups will compile the results into a presentation where they will discuss the processes used, the challenges encountered, and the conclusions about the usefulness of knowing how to calculate the volume of cylinders.

The project will be based on the application of the cylinder volume formula (V = πr²h), and on understanding the application of this formula in real situations. Each group will need a tape measure or ruler to measure the chosen cylindrical objects.

Required Materials

• Various cylindrical objects (food cans, water bottles, cardboard tubes, etc)
• Tape measure or ruler
• Calculator
• Material for the presentation (Can be PowerPoint, Google Slides, Prezi, etc.)

Step by Step

1. In groups of 3 to 5 people, identify at least 5 cylindrical objects in your homes or communities that can be measured.

2. Use the tape measure or ruler to measure the radius (or diameter) and height of each object.

3. Calculate the volume of each object using the cylinder volume formula: V = πr²h.

4. Document the entire process: the chosen objects, their measurements, and how you calculated the volume.

5. Prepare a presentation based on your findings. Include images of the chosen objects, the measurements, the volume calculations performed, and conclusions about the importance and applications of calculating cylinder volume in everyday situations.

Project Deliverables

Students must deliver the prepared presentation and a written report:

1. Presentation: each group must prepare a presentation showing the chosen cylindrical objects, explaining how they arrived at the measurements and volume, and discussing the importance of calculating cylinder volume in everyday life.

2. Report: in addition to the presentation, each group must produce a written report following the following structure:

   • Introduction: Explain the project's objective, the relevance of calculating cylinder volume, and the real-life application.
   • Development: In this section, students must present the applied theory (calculation of cylinder volume), describe the activity performed, present the measurements taken and the calculations performed. Additionally, they should discuss the process, the challenges encountered, and how they solved them.
   • Conclusions: Students must summarize the main points of the work, discussing what they learned throughout the project, the skills they developed, and the conclusions they drew from the process.
   • Bibliography: Indicate the resources and references used to carry out the project.