Formula for calculating the volume, lateral surface area, and total surface area of a cylinder

A cylinder is a common geometric shape widely used in various aspects of life. Formulas for calculating the lateral and total surface areas of a cylinder are often encountered in geometry problems requiring learners to compute and solve exercises within a specific space occupied by the cylinder.

Detailed formulas for calculating the area and volume of a circular cylinder

Additionally, the formulas for calculating the area and volume of a cylinder are also applied in solving more complex problems involving calculating the volume of a cube or the area of a rectangle. Explore the formula for calculating the volume of a cylinder and the most illustrative examples in calculating the area and volume of a cylinder.

1. What is a cylinder?

A cylinder is a shape defined by two circles with equal diameters and the lateral surface. 
A circular cylinder is formed by rotating a rectangle around a fixed axis, resulting in a cylinder. For further understanding of a circular cylinder, please refer to the Wikipedia article on circular cylinders.

2. Formulas and methods for calculating the surface area of a cylinder

The surface area of a cylinder is the entire space occupied by calculating the sum of the lateral surface area and the area of the two bases. Meanwhile, the total surface area of a cylinder is the area of the lateral surface of the cylinder, excluding the area of the two bases.

2.1. Formula for calculating the lateral surface area of a cylinder

+ r: cylinder radius
+ h: height from the base to the top of the cylinder (also known as the generatrix)

2.2. Formula for calculating the total surface area of a cylinder

Where:

+ r: cylinder radius
+ 2 x π x r x h: lateral surface area of the cylinder
+ 2 x π x r2: area of the two bases

2.3. Example of calculating the surface area of a cylinder

* Example 1: Consider a cylinder with a circular base radius of 6 cm, and a height from the base to the top of the cylinder of 8 cm. What are the lateral surface area and total surface area of the cylinder?

According to the formula, we have the base circle radius r = 6 cm and the height of the cylinder h = 8 cm . Hence, we can calculate the lateral surface area and total surface area of the cylinder as follows:

- Lateral surface area of the cylinder = 2 x π x r x h = 2 x π x 6 x 8 = ~ 301 cm²

- Total surface area of the cylinder = 2 π x r x (r + h) = 2 x π x 6 x (6 + 8) = ~ 527 cm²

Example 2: Calculate the lateral surface area of a cylinder with a radius of 2 and a height of 4.

Applying the formula, we can similarly calculate the lateral surface area of the cylinder as: 50.24

* Example 3: Calculate the lateral surface area of a cylinder with a height of 20m and a circumference of the base equal to 5m

Note: In addition to the aforementioned exercises calculating the lateral surface area of cylinders, 9th-grade mathematics also commonly includes exercises requiring the calculation of the lateral surface area of cylinders with a generatrix and base radius r. Here, the generatrix is understood as the height of the prism. Students can substitute values into the formula and calculate as usual.

3. Volume Calculation Formulas and Methods for a Cylinder

The volume of a cylinder is the amount of space occupied by a certain cylinder. The volume of a cylinder is measured in cubic units (cubic distance).

3.1. Formula for Calculating the Volume of a Cylinder

Where:

- r: cylinder radius
- h: cylinder height

3.2. Example of Calculating the Volume of a Cylinder

For any given cylinder with a base radius r = 4 cm and a height from the top to the base of the cylinder h = 8 cm. What is the volume of this cylinder?

Accordingly, we apply the formula for calculating the volume of a cylinder, where the base circle radius of the cylinder r = 4cm and the height of the cylinder h = 8cm. Therefore, we have the formula for calculating the volume of the cylinder as follows:

V = π x r2 x h = π x 42 x 8 = ~ 402 cm³

Following the instructions of this article, readers have gained a better understanding of the formulas for calculating the surface area and volume of a cylinder, especially with the commonly used formula for calculating the surface area of a cylinder in geometry-related articles. Also, with the formula for calculating the volume of a cylinder, you will easily notice in exercises combined with calculating the volume of a cube or the volume of a rectangular box.

Furthermore, in their studies, students will also become familiar with parallelograms, similar to cylinders, which will involve formulas for calculating the area and perimeter of parallelograms ..  refer to the formula for calculating the area of a parallelogram to study better.

Wishing you success!