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The formula for the area and volume of a cylinder

The law of the area and volume of a cylinder has always been important in our practical and scientific lives.

We encounter geometric shapes in our ordinary days, whether they are simple, complex, or the most complex, such as land areas, water bottles, and even buildings and towers.

The study of these shapes and models does not concern only students and mathematicians. All we learn is It is linked to what is around us, and in this article today via the reference website, we will talk about the law of the area and volume of a cylinder, the method of calculating it, its circumference, and everything related to it, and what matters to our dear readers to know about this subject.

area law

The simple law of area, as we learned in the classroom, is defined as the total area of ​​any two-dimensional shape occupied by any object or shape.

Which is calculated by multiplying the dimensions of the geometric figure in front of us by each other. For example, the area of ​​a rectangle is the product of multiplying the length by the width, which will give us the total number of squares of which the rectangle is, if its length is 5 meters and its width is 3 meters, the result will be: 5 x 3 = 15, and therefore this will be The result is the number of small squares that make up the large area, each of which is only one square meter.

Volume Law 

The volume represents to us the three-dimensional image that belongs to every object or body around us and includes a space of space. It refers to the total amount of space surrounding the closed surface.

For example, a water bottle is a three-dimensional volume or water tanks and other things that we find around us, and the unit of measurement used in volume is The cubic meter, unlike the physical area, is taken in square meters, and in a simpler formula, it can be said that the volume determines the total capacity owned by the physical body that places and what it contains to fill the void, for example, a football or basketball has a certain amount of air and this quantity is determined by the volume, the volume of a rectangular water tank It is the amount of water inside it, which is calculated in cubic meters.

Just as the formula for the square meter in the area of ​​a regular rectangle expresses the number of its constituent squares, as we mentioned in the previous example, the volume of the rectangular prism represented by the tank is calculated by the number of cubic squares that make up it, so that its volume is the result of calculating all its sides. represented by its heroism and its width.

The formula for the area and volume of a cylinder

A cylinder is scientifically defined as two parallel circles of the same size located at the top and bottom of the circular body, which is called the bases of the cylinder. As for the cylinder body, it is the height that connects the two bases at the top and bottom. He will not see the gas cylinder in homes or circular-shaped tanks on the roofs of buildings, and this is a vivid and realistic example of these objects.

Total and lateral cylinder area

As we mentioned that the outer cylinder body consists of two areas, the bases and the raised oriented body between them, but at the beginning, we must get acquainted with some arithmetic terms, which are the semicircle and symbolized by r, the height, and symbolized by h, and π, which is used in calculating the area and perimeter of circles and equal to 3.14 or 22/7, and according to the mathematical laws, the arithmetic process will be as follows:

  1. Lateral area of ​​the base: this includes calculating the two bases of the cylinder according to the following equation: 2πr 2 which means 2 x 3.14 x radius x radius
  2. Lateral area of ​​the body: It is the calculation of the curved body connecting the two bases according to the following equation: 2πrh, which means 2 x 3.14 x height x radius
  3. Total area: It is the final result of combining the lateral area of ​​the base and the lateral area of ​​the body according to the following equation: 2πr 2 + 2πrh which means 2 x 3.14 x radius x radius + 2 x 3.14 x radius x height

What is the volume formula for a cylinder?

The volume of the cylinder is a term that expresses the amount that the body acquires from the void, and in other words, it can be said that the volume of the cylinder is the amount of void within the lateral and total space of it. , and it is calculated by multiplying the area of ​​the lower and upper bases by the height, and since the area of ​​the two bases is 2πr 2, this means that the volume is equal to 2πr 2h, which means 2 x 3.14 x radius x radius x-height, and in other cases, this law may differ somewhat from Were the type and structure of the cylindrical body, which we will learn about later.

Cylinder types

In geometry, there is often a specific volume for each cylinder and a specific area, but not all areas and volumes are calculated in the same way. Although a cylinder is a three-dimensional shape defined by two parallel identical bases, it sometimes has other types that differ in the way of calculating them, and below we present to you the types Different types of cylinders are the following:

  1. Right circular cylinder: It is a cylinder whose bases are usually circles and each straight segment forms part of the curved lateral surface perpendicular to the bases.
  2. Inclined cylinder: It is a cylinder whose sides are inclined above the base at an angle not equal to the right angle.
  3. Elliptical cylinder: a cylinder whose bases are usually oval.
  4. Hollow cylinder: It is a hollow cylinder that has two empty bases and is shaped like a tube.

An example of the lateral and total area of ​​a cylinder 

After we know the mathematical formulas for calculating the area of ​​a lateral and total cylinder, we will present the following example to understand this formula well. If we have a cylinder with a radius of 5 cm and a height of 10 cm, and we know that its formula is 2πr 2, then the area of ​​the base will be as follows:

  • 2×3.14×5×5=157

The lateral area of ​​2πrh will be:

  • 2×3.14×5×10=314

So the total area of ​​the cylinder will be the base area + the lateral area according to the following: 

  • 2×3.14×5×5 + 2×3.14×5×10= 157+314 = 471

An example of calculating the volume of a cylinder

The volume of the cylinder is to calculate the area of ​​the base 2πr 2 multiplied by the height h to get the equation 2πr2 h. If we have a cylindrical shape with a height of 7 cm and a radius of 5 cm, the solution will be as follows:

  • 2×3.14×5×5×7 = 1570