Cylinder explanation

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In the next
presentation we find the definition of the cylinder. In which you can identify your
elements. Also the formulas to find the volume and area of the cylinder.
Created by Monica Moreno Vargas

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mathematics

11º - Secundaria

geometría del espacio

solido cilindro

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Cylinder explanation Versión en línea In the next presentation we find the definition of the cylinder. In which you can identify your elements. Also the formulas to find the volume and area of the cylinder. Created by Monica Moreno Vargas por Geometria Del espacio 1 What is the cylinder? A cylinder is a geometric body that is made up of a rectangle that rotates around one of its sides. In mathematics, it is also defined as the cylindrical surface that is formed when a line called the generatrix rotates around another parallel line, which we call the axis. Cylinder typesThere are two types of cylinder: Rectangular cylinder When the axis of the cylinder is perpendicular to the bases. Oblique cylinder If the axis is not perpendicular to the bases. Fernandez.C.(2021).Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/ 2 What is the cylinder? 3 Cylinder elements Axis: It is the fixed side around which the rectangle rotates. Bases : They are the circles that generate the sides perpendicular to the axis. Height : It is the distance between the two bases. Generatrix : It is the side opposite the axis, and it is the side that generates the cylinder. The generatrix of the cylinder is equal to the height. h = g SuperProf.(2021).Que significa Cilindro en Matemáticas.[Pagina Web]https://www.superprof.es/diccionario/matem.aticas/geometria/cilindro.html 4 Area of a cylinder How to calculate the area of a cylinder? We must take into account the development of the cylinder and calculate the area of its parts, that is, the rectangle and the two bases. Area of the rectangle = 2 × π × r × h Base area = π × r2 Adding everything we get the area = 2 × π × r × h + 2 × π × r2 Formula para calcular el area es: Área = 2 × π × r × ( h + r ) Fernandez. C.(2021). Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/ 5 Surface Area of a Cylinder 6 Example of cylinder area Example of cylinder area Calculate the area of a cylinder with radius 3 cm and height 60 mm. First, we must put both the radius and the height in the same units. So we have to change the height from millimeters to centimeters. If you want you can see our post on problems of conversion of measures of length that will help you refresh your memory to make the change of units. 60mm = 6cm Now, we are going to calculate the area of the rectangle that is equal to the lateral surface of the cylinder. As we had already indicated its formula before, we substitute it for the values of the cylinder: Area of the rectangle = 2 × π × r × h2 × 3.14 × 3 × 6 = 113.04 cm² Next, we have to calculate the area of the bases, which is equal to the area of a base but by 2. We take the formula that we had already indicated at the beginning and we also substitute the values: Base area = 2 × π × r22 × 3.14 × 9 = 56.52 cm² And to finish, we add the parts of the cylinder, that is, the lateral area that is the area of the rectangle and the area of the bases: Cylinder area = 2 × π × r × h + 2 × π × r2113.04 + 56.52 = 169.56 cm² Fernandez. C.(2021). Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/ 7 CYLINDER VOLUME The volume is equal to the area of the base times the height, remember that we usually indicate the height with the letter "h". Volume = π × r2 × h Fernandez. C.(2021). Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/ 8 CYLINDER VOLUME 9 Cylinder volume example Calculate the volume of a cylinder with radius 5 cm and height 60 mm. As we have indicated before, we must put both the radius and the height in the same units. We change the height from millimeters to centimeters: 60mm = 6cm To calculate the area of the base we multiply the radius squared by π: Base area = π × r2 3.14 × 25 = 78.50 cm² And to find the volume of the cylinder we have to multiply the area of the base by 6 cm which is what the height measures: 78.50 × 6 = 471 cm³ To calculate this volume we have multiplied an area (square units) by a height (linear units), that is why we have obtained cubic units. Remember that the unit of measurement for volume in the International System of Units is the cubic meter (m³), although we have used cm³, which is a submultiple of it. What we have calculated is valid whether the cylinder is straight or an oblique cylinder. Think about it, it is as if the tower of coins with which we represented an oblique cylinder were put straight, they would both have the same volume. Fernandez. C.(2021). Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/ 10 cylinders in everyday life The cylinder Can Be Represented Easy In Everyday Life example: Some Buildings Are Cylinder Shaped The coins Food and oil cans In Some Football Stadiums The candles Perforators Some Turbines and Motors

Cylinder explanation Versión en línea

In the next presentation we find the definition of the cylinder. In which you can identify your elements. Also the formulas to find the volume and area of the cylinder. Created by Monica Moreno Vargas

por Geometria Del espacio

What is the cylinder?

A cylinder is a geometric body that is made up of a rectangle that rotates around one of its sides. In mathematics, it is also defined as the cylindrical surface that is formed when a line called the generatrix rotates around another parallel line, which we call the axis.

Cylinder typesThere are two types of cylinder:

Rectangular cylinder When the axis of the cylinder is perpendicular to the bases.

Oblique cylinder If the axis is not perpendicular to the bases.

Fernandez.C.(2021).Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/

What is the cylinder?

Cylinder elements

Axis: It is the fixed side around which the rectangle rotates.

Bases : They are the circles that generate the sides perpendicular to the axis.

Height : It is the distance between the two bases.

Generatrix : It is the side opposite the axis, and it is the side that generates the cylinder. The generatrix of the cylinder is equal to the height. h = g

SuperProf.(2021).Que significa Cilindro en Matemáticas.[Pagina Web]https://www.superprof.es/diccionario/matem.aticas/geometria/cilindro.html

Area of a cylinder

How to calculate the area of a cylinder?
We must take into account the development of the cylinder and calculate the area of its parts, that is, the rectangle and the two bases.
Area of the rectangle = 2 × π × r × h
Base area = π × r2

Adding everything we get the area = 2 × π × r × h + 2 × π × r2

Formula para calcular el area es:
Área = 2 × π × r × ( h + r )

Fernandez. C.(2021). Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/

Surface Area of a Cylinder

Example of cylinder area

Example of cylinder area
Calculate the area of a cylinder with radius 3 cm and height 60 mm.
First, we must put both the radius and the height in the same units. So we have to change the height from millimeters to centimeters. If you want you can see our post on problems of conversion of measures of length that will help you refresh your memory to make the change of units.
60mm = 6cm
Now, we are going to calculate the area of the rectangle that is equal to the lateral surface of the cylinder. As we had already indicated its formula before, we substitute it for the values of the cylinder:
Area of the rectangle = 2 × π × r × h2 × 3.14 × 3 × 6 = 113.04 cm²
Next, we have to calculate the area of the bases, which is equal to the area of a base but by 2.
We take the formula that we had already indicated at the beginning and we also substitute the values:
Base area = 2 × π × r22 × 3.14 × 9 = 56.52 cm²
And to finish, we add the parts of the cylinder, that is, the lateral area that is the area of the rectangle and the area of the bases:
Cylinder area = 2 × π × r × h + 2 × π × r2113.04 + 56.52 = 169.56 cm²

Fernandez. C.(2021). Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/

CYLINDER VOLUME

The volume is equal to the area of the base times the height, remember that we usually indicate the height with the letter "h".

Volume = π × r2 × h

Fernandez. C.(2021). Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/

CYLINDER VOLUME

Cylinder volume example

Calculate the volume of a cylinder with radius 5 cm and height 60 mm.
As we have indicated before, we must put both the radius and the height in the same units. We change the height from millimeters to centimeters:
60mm = 6cm

To calculate the area of the base we multiply the radius squared by π:

Base area = π × r2
3.14 × 25 = 78.50 cm²

And to find the volume of the cylinder we have to multiply the area of the base by 6 cm which is what the height measures:
78.50 × 6 = 471 cm³
To calculate this volume we have multiplied an area (square units) by a height (linear units), that is why we have obtained cubic units.

Remember that the unit of measurement for volume in the International System of Units is the cubic meter (m³), although we have used cm³, which is a submultiple of it.

What we have calculated is valid whether the cylinder is straight or an oblique cylinder.

Think about it, it is as if the tower of coins with which we represented an oblique cylinder were put straight, they would both have the same volume.

Fernandez. C.(2021). Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de.

https://www.smartick.es/blog/matematicas/geometria/cilindros/

Cylinder explanation

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Cylinder explanation Versión en línea

por Geometria Del espacio

What is the cylinder?

A cylinder is a geometric body that is made up of a rectangle that rotates around one of its sides. In mathematics, it is also defined as the cylindrical surface that is formed when a line called the generatrix rotates around another parallel line, which we call the axis.

Cylinder typesThere are two types of cylinder:

Rectangular cylinder When the axis of the cylinder is perpendicular to the bases.

Oblique cylinder If the axis is not perpendicular to the bases.

Fernandez.C.(2021).Cilindro: características, ejemplos y cómo calcular área y volumen. Recuperado de. https://www.smartick.es/blog/matematicas/geometria/cilindros/

What is the cylinder?

Cylinder elements

Axis: It is the fixed side around which the rectangle rotates.

Bases : They are the circles that generate the sides perpendicular to the axis.

Height : It is the distance between the two bases.

Generatrix : It is the side opposite the axis, and it is the side that generates the cylinder. The generatrix of the cylinder is equal to the height. h = g

Area of a cylinder

Formula para calcular el area es:Área = 2 × π × r × ( h + r )

Surface Area of a Cylinder

Example of cylinder area

CYLINDER VOLUME

The volume is equal to the area of the base times the height, remember that we usually indicate the height with the letter "h".

Volume = π × r2 × h

CYLINDER VOLUME

Cylinder volume example

Calculate the volume of a cylinder with radius 5 cm and height 60 mm.As we have indicated before, we must put both the radius and the height in the same units. We change the height from millimeters to centimeters:60mm = 6cm

To calculate the area of ​​the base we multiply the radius squared by π:

Base area = π × r23.14 × 25 = 78.50 cm²

And to find the volume of the cylinder we have to multiply the area of ​​the base by 6 cm which is what the height measures:78.50 × 6 = 471 cm³ To calculate this volume we have multiplied an area (square units) by a height (linear units), that is why we have obtained cubic units.

Remember that the unit of measurement for volume in the International System of Units is the cubic meter (m³), although we have used cm³, which is a submultiple of it.

What we have calculated is valid whether the cylinder is straight or an oblique cylinder.

Think about it, it is as if the tower of coins with which we represented an oblique cylinder were put straight, they would both have the same volume.

cylinders in everyday life

The cylinder Can Be Represented Easy In Everyday Life

example:

Some Buildings Are Cylinder Shaped

The coins

Food and oil cans

In Some Football Stadiums

The candles

Perforators

Some Turbines and Motors

Formula para calcular el area es:
Área = 2 × π × r × ( h + r )

Calculate the volume of a cylinder with radius 5 cm and height 60 mm.
As we have indicated before, we must put both the radius and the height in the same units. We change the height from millimeters to centimeters:
60mm = 6cm

To calculate the area of the base we multiply the radius squared by π:

Base area = π × r2
3.14 × 25 = 78.50 cm²

And to find the volume of the cylinder we have to multiply the area of the base by 6 cm which is what the height measures:
78.50 × 6 = 471 cm³
To calculate this volume we have multiplied an area (square units) by a height (linear units), that is why we have obtained cubic units.