Contextualization
Mathematics is a science that is present in every action of our daily life, whether through financial calculation for the acquisition of a product or in the measurement of a quantity necessary for the preparation of a recipe, for example. In this sense, one of the mathematical topics that has wide practical application is the study of geometric solids and the concepts related to volume and surface area measures, in particular, the cylinder.
A cylinder is a three-dimensional geometric figure formed by two bases that are congruent circles and a lateral surface, these parts being fundamental to the understanding of the concepts of volume and total area of this solid. By understanding and applying these concepts correctly, we can solve a variety of practical problems.
Introduction
The mathematical definition of a cylinder tells us that it is a solid that is formed when all the parallel lines drawn from the edge of one circle to another are of the same length. This is what gives the cylinder its characteristic shape. Within mathematics, cylinders are important because they are useful for modeling a number of real-world situations. For example, calculating the volume of a cylinder can help us determine the capacity of a barrel, a can of soda, a cylindrical pool, etc.
The surface area of a cylinder is also an important concept. Knowing how to calculate this area allows us to determine, for example, the amount of material needed to build a barrel or the amount of paper needed to wrap a cylinder.
Hands-on Activity: "Creating and Investigating Cylinders"
Project Objective
The objective of this project is for students to develop skills in calculating the surface area and volume of cylinders, as well as to understand how these concepts apply to the real world, by creating their own cylinder models.
Project Description
Students work in teams of 3-5. Each team will be responsible for producing 3-5 different cylinders (one per team member) using the materials provided. They will carefully measure the dimensions of their cylinders, perform the necessary calculations to determine surface areas and volumes, and produce a detailed report of their findings.
Materials
- Cardstock or cardboard
- Measuring tape or ruler
- Scissors
- Pen or pencil
- Calculator
Procedure
- Each team member will create one cylinder using the cardstock or cardboard. They are free to choose the size of their cylinder, but each needs to be different.
- Once their cylinders are complete, students will need to measure and record the dimensions (base radius and height) of their cylinders.
- Using the dimensions they recorded, students will calculate the surface area and volume of each of their cylinders.
- For each cylinder, students should discuss and document potential real-world applications.
- Finally, each team will produce a detailed report that includes all of the measurements, calculations, and applications for each cylinder. The team's discussion of the real-world applications should also be documented.
Project Deliverables
Project deliverables include the constructed cylinders, calculations for their measurements (surface area and volume), and a report.
The report should include:
- Introduction: Contextualization of the project and the importance and applicability of studying the volume and area of cylinders.
- Development: A detailed description of how each cylinder was made, including the measurements, the calculations for surface area and volume, and the methodology used. The team's discussions and conclusions about the real-world applications of the cylinders should also be included in this section.
- Conclusions: A review of the project, reflections on what was learned during the course of the project, and any new questions or ideas that may have arisen during the process.
- Bibliography: References for any sources that were used to assist in the project.
The project will take place over the course of one month and each student should expect to spend five to ten hours completing all aspects of the project.
