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Cylinder

A cylinder is a three-dimensional solid figure with two identical circular bases connected by a curving surface at a specific distance from the cylinder’s center, which is the cylinder’s height. Real-life cylinders include toilet paper rolls and cold drink cans. Do you know that the Leaning Tower of Pisa is shaped like a cylinder? Today, we will learn more about the cylinder shape.

Definition of a cylinder

A cylinder is a three-dimensional solid structure made up of two identical, parallel bases connected by a curved surface. These bases have the appearance of circular discs. The axis of the cylinder shape is a line that runs from the center or connects the centers of two circular bases. The height, “h,” represents the distance between the two bases, which is known as perpendicular distance. The radius of the cylinder, denoted by “r,” is the distance between the center and the outer limit of the two circular bases. The cylinder is made up of two circles and one rectangle. Some real-life examples of cylinder shapes are pipes, fire extinguishers, water tanks, cold-drink cans, etc.

Types of Cylinder

We just read about some real-life examples of a cylinder, which shows that it can be of various types. In geometry, there are four different types of cylinders. They are as follows:

  • Right Circular Cylinder: A right circular cylinder is one in which the axis of two parallel bases is perpendicular to the center of the base.
  • Cylinder Oblique: The sides of an oblique cylinder lean over the base. The sides are not perpendicular to the center of the base in this case. The Leaning Tower of Pisa is an oblique cylinder in the real world.
  • Elliptic Cylinder: An elliptic cylinder is defined as a cylinder with an elliptic base.
  • Cylindrical Shell or Right Circular Hollow Cylinder: It is made up of two right circular cylinders that are bound within each other. The axis has a common point that is perpendicular to the central base. It differs from the right circular cylinder since it is hollow inside, meaning there is some space or void.

Properties of cylinder

Every geometrical shape has unique qualities or properties that distinguish it from other figures. Let’s look at some of the qualities of a cylinder form, which are stated below:

  • A cylinder has one curved surface and two identical flat faces.
  • The two circular bases are identical in size.
  • The radius of the base and the height of the curved surface determine its size.
  • A cylinder, unlike a cone, cube, or cuboid, has no vertex. It indicates that the cylinder lacks a specified corner.
  • The cylinder’s base and top are identical, that is, it has the same round or elliptical base.

Equations of cylinder

Surface area and volume are the two most important formulas in every three-dimensional geometric figure:

 Similarly, the cylinder’s surface areas and volume are determined by three primary formulas.

  • Curved surface area or Lateral surface area
  • The total area of surface
  • Volume

Curved Surface Area of Cylinder:

The curved surface area is also termed lateral surface area. The area formed by the curved surface of the cylinder i.e. space occupied between the two parallel circular bases is known as its CSA. The formula for cylinder curved surface area is given as,

Curved Surface Area (CSA) = 2πrh square units

(Note: ‘h’ is the height, ‘r’ is the radius, and the value of π is 22/7 or 3.14 approximately).

Total Surface Area of Cylinder:

The total surface area defines the total area that it occupies including the bases. The cylinder consists of two circles and one curved sheet. So, to find out the total surface area of a cylinder, we calculate the curved surface area and the area of two circles.

Curved Surface Area (CSA) = Circumference × Height

CSA= 2πr × h

Area of circle = πr2

Total Surface Area (TSA) = Curved Surface Area + 2(Area of a circle)

Total Surface Area (TSA) = 2πrh + 2πr2 = 2πr(h+r) square units

(Note- ‘h’ is the height and ‘r’ is the radius. There are two circles, so we multiply the area of the base circle by 2)

Net of a Cylinder:

The net of a cylinder is a 2D structure made by unfolding it. It helps us to visualize the shape of a cylinder and its surface area. When we unfold a cylinder, we get a rectangle joined by two identical circles that form the top and the bottom bases of the cylinder shape.      

       Cylinder Examples:

Example 1: Britt wants to buy a can that can hold 1 gallon of oil. The radius of the can is 5 inches. Help Britt find the height of the can she has to buy. Hint: The can is in the form of a cylinder.
Solution:
Volume, V = 1 gallon
1 gallon = 231 cubic inches
Radius, r = 5 inches (given)
The volume of a cylinder, V = πr2h
By substituting the values in the volume formula, we get,
231 = 22/7 × (5)2 × h
(231 × 7)/(22 × 25) = h
h = 2.94 inches
Therefore, the height of the can should be 2.94 inches.

Example 2. Emma has an old cylindrical water tank at her home. The radius is 40 inches and the height is 150 inches. She wants to replace it with a new one with the same dimensions. Help Emma figure out the area of the water tank.
Solution:
The water tank is in the form of a cylinder.
Total surface area of a cylinder = 2πr(h+r)
By substituting the values given in the question in this formula, we get,
TSA = 2 × 22/7 × 40 (150 + 40)
TSA = 2 × 22/7 × 7600
TSA = 47,771.42 sq. inches
Therefore, the area of the water tank = 47,771.42 sq. inches.

Example 3. What is the volume of the cylinder with a radius of 5 units and a height of 8 units?
Solution:
Radius, r = 5 units
Height, h = 8 units
The volume of the cylinder, V = πr2h cubic units
V = (22/7) × 52 × 8
V = 22/7 × 25 × 8
V= 628.57 cubic units.
Therefore, the required volume is 628.57 cubic units.

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