Properties of Cylinder
A cylinder is a solid, three-dimensional shape made up of two bases that are both identical circles joined by a curved surface that is positioned at a certain height from the centre. Rolls of toilet paper and beverage cans are examples of real-world cylinders. Unexpectedly, the Leaning Tower of Pisa has a cylindrical shape as well. The word “cylinder” comes from the Greek word “kylindros,” which also means “roll” or “roller.” Originally, this term was applied to solid figures with circular bases and straight sides in mathematics to describe their geometric shape. Later, the phrase was expanded to include other cylindrical items including pipes, containers, and engine components. The cylinder shape will be discussed in more detail in this article.
Definition of Cylinder
The solid three-dimensional shape of a cylinder is made up of two identical circular bases that are parallel to one another and are joined by a curved surface. The axis of the cylinder shape is a line that connects the centres of the two circular bases or runs through their centres. Height is denoted by the letter “h” and is the perpendicular distance between the two bases. The distance between the cylinder’s centre and its outer boundary—represented by the symbol “r”—is its radius. Two circles and one rectangle unite to form the cylinder’s overall shape. For a visual representation of the cylinder shape, see the related image.
Cylinder Faces Vertices Edges
Three surfaces make up a cylinder, two of which are circular faces that are congruent and are positioned at the opposite ends of the cylinder. The third surface, which is curved, links the two circular faces. The curved surface resembles a rectangle that has been rolled up into a tube. A cylinder contains a total of 3 faces (2 round faces and 1 curved face), 2 edges (placed at the top and bottom), and 0 vertices (because the cylinder’s two edges do not intersect anywhere).
Properties of Cylinder
Every geometrical figure has particular traits and qualities that set it apart from other shapes. Additionally, the cylinder shape has distinctive characteristics, some of which are listed below:
1.Two equal flat faces and one curving surface make up a cylinder.
2.The size and shape of the two circular bases are identical.
3.The radius of the base and the height of the curved surface both affect the cylinder’s size.
4.A cylinder has no distinct corners because it lacks vertices, unlike shapes like cones, cubes, and cuboids.
5.The cylinder’s top and bottom surfaces are identical in size and shape, being either round or elliptical.
Types of Cylinder
Since there are many different types of cylinders in the real world, we have learned about a variety of them. There are four different kinds of cylinders in geometry, and they are as follows:
1.The right circular cylinder has parallel bases and an axis that is perpendicular to the base’s middle. A soda can is an illustration of a right circular cylinder.
2.Oblique Cylinder: An oblique cylinder is one with sides that slope over the base and are not parallel to the base’s centre. An illustration of an oblique cylinder is the Leaning Tower of Pisa.
3.Elliptic Cylinder: An elliptic cylinder is a type of cylinder that has an elliptical base. An optical lens is an illustration of an elliptic cylinder.
Formulas
We have the calculations based on the cylinder’s two main components.
Curved surface area or laterally flat surface area
Surface Area Overall
Curved Surface Area of Cylinder
A cylinder’s curved surface area is the region of its lateral surface that is located in between its two parallel circular bases. This can be stated using the following formula:
Curved Surface Area is equal to two rh square units.
On the other hand, a cylinder’s total surface area is equal to the sum of the areas of its two circular bases and its curved surface area. It is illustrative of:
TSA = Area of Circular Bases + Curved Surface Area
TSA = 2rh plus 2r2.
Since 2r appears frequently in the expression above, we can simplify it as follows:
A = 2r(r+h) square units of total surface area
Volume of Cylinder
Every three-dimensional item has a volume, which is a measure of how much space it takes up. The area occupied by a cylinder in any three-dimensional plane is known as its volume. The volume of a cylinder also indicates how much water it can store when submerged entirely. The following is the formula for a cylinder’s volume:
Volume is equal to r2h cubic units.
where “h” is the height of the cylinder and “r” is the radius of the circular base.
Volume of the Cylinder, V = πr2h cubic units
Solved Examples
Question 1
To determine the total surface area of a cylinder with a radius of 5cm and a height of 10cm, we can use the formula:
Total surface area of a cylinder, A = 2πr(r+h) square units
Plugging in the values given, we get:
A = 2π × 5(5 + 10) = 2π × 5(15) = 2π × 75
Evaluating this expression, we get:
A = 150π
Approximating π as 3.14, we get:
A = 471 cm^2
Hence, the total surface area of the given cylinder is approximately 471 cm^2.
Question 2
What is the volume of a cylindrical water container with a height of 7cm and a diameter of 10cm?
Given that the diameter of the container is 10cm, we can determine its radius as half of the diameter, which is 5cm. The height of the container is 7cm.
Using the formula for the volume of a cylinder:
Volume = πr^2h cubic units
Plugging in the values we have:
Volume = π × 5^2 × 7
Volume = π × 25 × 7 = (22/7) × 25 × 7 = 22 × 25
Therefore, the volume of the water container is 550 cubic centimeters (cm^3).
Frequently Asked Questions – FAQs
A cylinder has a curved surface and two parallel circular bottoms. The height of the cylinder is equal to the angle at which the two bases are perpendicular. The axis of a cylinder is the line segment connecting the centres of two bases.
Examples of cylinders in everyday life include gas cylinders, fire extinguishers, cans, pipes, etc.
A cylinder is having two circular bases.
