Cylinders are solid shapes that have intrigued mathematicians and physicists for centuries due to their simplicity and real-world applications. This three-dimensional figure is characterized by its two parallel circular bases and its side surface that curves in the shape of a stretched rectangle. In this article, we will explore the properties and applications of cylinders as geometric figures, highlighting their importance in the study of geometry and physics.
Parts
To fully understand the geometric figure of a cylinder, it is crucial to analyze its fundamental parts:
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Circular Bases: The cylinder has two bases that are perfect circles. These bases are identical in size and are lined up one on top of the other in parallel.
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Side Surface: The side surface of the cylinder resembles a rectangle that has been rolled around the circular bases. The height of the rectangle is equal to the distance between the bases, and its length is the circumference of one of the bases.
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Axis: The axis of the cylinder is a straight line connecting the center of both bases. This axis is crucial for defining the height and other properties of the cylinder.
Properties
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Height: The height of a cylinder is the distance between the two circular bases. It is an important factor in volume and area calculations.
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Radius: The radius of a cylinder is the distance from the center of one of the circular bases to the edge of the base. This value is used in area and volume calculations.
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Volume Compared to a Cone: The volume of a cylinder is one third the volume of a cone that shares the same base and height.
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Versatility: In the context of mechanical devices, such as hydraulic or pneumatic cylinders, these are essential for converting fluid pressure into linear motion, making them essential in industry and engineering.
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Diverse Applications: Cylinders have a wide range of applications in everyday life, from packages and containers to automotive suspension systems, industrial machinery and construction lifting systems.
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Simplicity and Efficiency: Cylinders are prized for their simple yet effective design, allowing a variety of tasks to be performed with efficiency and precision.
Volume
The volume of a cylinder is calculated using the following formula:
V=π·r2·h
Where:
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V is the volume of the cylinder.
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π (pi) is a mathematical constant approximately equal to 3.14159.
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r is the radius of one of the circular bases of the cylinder.
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h is the height of the cylinder.
To calculate the volume of a cylinder, you simply have to know the value of the radius of one of the bases and the height of the cylinder, then substitute these values in the formula and carry out the mathematical operation.
Surface area
The lateral surface area of a cylinder, called the lateral area, is calculated using the following formula:
A=2·π·r·h
Where:
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A is the lateral area of the cylinder.
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π (pi) is a mathematical constant approximately equal to 3.14159.
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r is the radius of one of the circular bases of the cylinder.
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h is the height of the cylinder.
This formula calculates the area of the curved part of the cylinder. If you want to calculate the total surface area of the cylinder, which includes the two circular bases, you must add the area of the two bases to the lateral area:
Atotal =2·π·r·h+2·π·r2
To calculate the lateral area of a cylinder, you simply have to know the value of the radius of one of the bases and the height of the cylinder, and then substitute these values into the corresponding formula.
Real life applications
The geometric figure of the cylinder has significant applications in the real world:
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Jars and Containers: Many jars and containers used in industry, such as soft drink cans and gas cylinders, are cylindrical in shape due to their space efficiency and ease of manufacture.
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Machines and Engines: Cylinders are found in internal combustion engines and hydraulic systems, where they are used to convert fluid pressure into linear motion.
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Construction: Cylinders are essential in the construction of structures such as columns and piles, where they provide vertical support and stability.
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Mathematics and Physics: Cylinders are a fundamental geometric figure in geometry and have applications in physics in areas such as fluid dynamics and the theory of relativity.
Conclusion
Cylinders are fascinating geometric figures that play a crucial role in both mathematics and physics. Their simplicity in design, with two circular bases and a curved side surface, hides a wealth of properties and applications that make them essential in a wide variety of fields.
Whether in everyday packaging or in complex mathematical equations, cylinders continue to be a geometric figure that inspires study and admiration in the world of science and engineering.