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# Cylinder|Definition & Meaning

## Definition

A **cylinder** is a special three-dimensional solid **geometrical** shape that consists of two flat **circles** at either end joined by a curved **surface**. The circles are referred to as the **bases** and the perpendicular distance between them represents the **height** of the cylinder.

## What Is a Cylinder?

A **cylinder** is a solid **geometrical** shape that comprises **two** flat and circular bodies at the ends, bounded by a **curved** surface at a particular **distance**. A cylinder is a **geometrical** figure in a 3-dimensional plane. The **circular** faces are the base of the **cylinder,** and the space or **length** between these two **bases** is called the **height**.

The bases are **identical** and parallel to each other. The **center** line merging the **circular** bases is the axis of the **cylinder**. The height is the **perpendicular** stretch between the bases. As the **bases** are circles, the **curved** surface is like a **rectangle;** hence the **cylinder** is a combined figure including **circles** and rectangles.

Unlike some other **3D** shapes, the number of **vertices** of a cylinder is **zero**. An **object** holding a shape like a **cylinder** is said to be **cylindrical**. Many daily life objects are cylindrical in **shape**, for example, wood logs, cells, cold drink cans, **pipes**, fire **extinguishers**, and many more.

## Properties of Cylinder

The most basic properties of a cylinder are as follows:

- It may consist of two
**flat**circular or**elliptical**bases. - Its curved surface joins the
**bases**of the cylinder. - The bases of a cylinder are invariably
**parallel**and**congruent**to each other. - It has 2 two curved
**edges**but no vertices. - The
**distance**of the bases from the center point to the**exterior**boundary is the radius of the cylinder. - The size of the
**cylinder**is determined by the radius and height. **Curved**surface area,**total**surface area, and**volume**of a cylinder can be estimated using radius and height.- Right
**Circular**cylinders,**oblique**cylinders, and**elliptical**cylinders are some of the kinds of cylinders. - A cylinder has two kinds of surface areas, i.e.,
**lateral**surface area and**total**surface area.

### The Volume of a Cylinder

It is the **portion** of space occupied by the **cylinder** in a 3-dimensional plane. The **volume** tells us how much of the **quantity** can be **stored** in the cylinder. It can be determined by **multiplying** the area of the **base,** i.e., πr^{2}, and height, i.e., h.

Cylindrical Volume = πr^{2}h

### Lateral Surface Area of a Cylinder

The portion of a **cylinder** that is slightly curved around the **edges** of the **rounded** area is represented as the **lateral surface.** It is the **amount** of space bounded between the borders of the **curved** area of the cylinder. **Lateral** surface area is also going by the name curved **surface** area. Using the formula given below, we can easily figure out the lateral area:

Cylindrical lateral area = 2πrh square units

Where r represents the **radius** and h stands for the **height** of the cylinder.

### The Total Surface Area of the Cylinder

As the name indicates, it is the **area** shielded by the **cylinder** as a whole. It includes the **area** of the **bases** as well as the area of the **curved** part of the cylinder. The **total** surface area is evaluated by the addition of the **lateral** surface area and the **area** of the bases.

Area of **circular** base = πr^{2}

Cylindrical lateral area = 2πrh square units

Since a cylinder has two **circular** bases, therefore we **multiply** the area of the circular base by 2.

**T****otal area of surface** = lateral area + 2(area of **circular** base) = 2πrh + 2(πr^{2})

**Absolute **cylindrical surface area = 2πr(h + r) **square** units

### The Radius of the Cylinder

The** Radius** of the cylinder is determined by finding the **radius** of its bases. It is the **length** from its center point to the outer **boundary**. Radius is generally denoted by **r**. It is usually **measured** in cm,m, mm, and ft. The formula for finding the **radius** can be evaluated using the formula for the **volume** of a cylinder:

The volume of the **cylinder** = V = πr^{2}h cubic units

r^{2} = V\πh

r = √V\πh

Where r **denotes** the radius, V is the volume, and h is the **height** of the cylinder.

### The Height of the Cylinder

The **height** is the measure of the **length** between the two **bases** of the cylinder. The notation used for **height** is h. The height is usually **measured** in m, cm, mm, and ft. The formula of **height** can also be determined by utilizing the equation provided below for the **cylindrical volume**:

The volume of the **cylinder **= V = πr^{2}h cubic units

H = V \ πr^{2}

Where h denotes the **height**, V is the **volume** of the cylinder, and r stands for the **radius** of the cylinder.

### Circumference of Cylinder

Since a **cylinder** includes circular **bases**, it also constitutes some **circumference**. The circumference of the **cylinder** is basically the **measure** of the length of the boundary of the circle. The **circumference** is measured in the **same** units as lengths. To estimate the circumference of a **cylinder**, we have the following formula:

Circumference of cylinder = 2πr

## Types of Cylinders

In geometry, there are four classifications of cylinders. Namely

**Right**circular cylinder- Oblique cylinder
**Elliptical**cylinder- Right circular hollow cylinder

Let us discuss the differences and descriptions of these cylinders.

### Right Circular Cylinder

A cylinder whose **axis** is at a 90-degree angle or **perpendicular** to the bases is known as a **right** cylinder. When the **bases** are circular in shape, it is named a right circular **cylinder**.

The volume of the right **circular** cylinder = πr^{2}h cubic units

Right circular cylinder surface area= 2πrh + 2πr^{2} **square** units

Right circular cylinder lateral area= 2πrh square units

### Oblique Cylinder

It is opposite to the right **circular** cylinder. The Oblique cylinder has no **perpendicular** axis; hence its sides **incline** over the base. Both **bases** are not directly in **front** of each other. It is a **tilted** or inclined form of a **circular** cylinder. The famous leaning tower of Pisa is an **oblique** cylinder.

The volume of the **oblique** cylinder = πr^{2}h cubic units

Total **Surface** area of the **oblique** cylinder = h + 2πr^{2} square units

**Lateral** surface area of the oblique cylinder = 2πrh **square** units

### Elliptical Cylinder

A cylinder whose **bases** are in the shape of an ellipse is known as an **elliptical** cylinder. Or we can also define it as a **cylinder** whose cross-section is an **ellipse** in shape.

The **volume** of the elliptical cylinder = πabL cubic units

Where a denotes the **semimajor** axis, b denotes the semiminor axis, and L is the **length** of the cylinder.

The **lateral** surface area of the **elliptical** cylinder = perimeter * height

Base area of the **elliptical** cylinder = abπ square units

Total **surface** area = 2A + L square units

Where A is the **base** area, and L is the **lateral** surface area.

### Right Circular Hollow Cylinder

It is a **cylinder** that comprises two **cylinders** in such a manner that one is **bordered** by the other. Both **cylinders** are right **circular** cylinders. This cylinder has one point of **the axis,** and it is also **perpendicular** to the center of the **base**.

The term **hollow** in the name of this cylinder is due to the reason that the **inner** part of the cylinder is **hollow**, unlike the right **circular** cylinder. The right circular hollow cylinder has another name, i.e., cylindrical **shell**.

The **volume** of the right circular hollow cylinder = π(R^{2 }– r^{2})h cubic units

Lateral **surface** area = 2πrh square units

**Base** surface area = πr^{2} square units

**Total** surface area of the right circular hollow cylinder = (2πrh + 2πr^{2}) **square** units

= 2πr(h + r) **square** units

### Net of a Cylinder

A **geometric net,** also referred to simply as a net, is a **two-dimensional** representation of a three-dimensional **geometric shape.** It displays what the **figure** would look like if its sides were **flattened** and all its faces were **visible.** In other words, it’s a pattern of a **solid** figure that can be folded into a **3D** shape.

Three-dimensional **figures** can be made by folding nets.** ****Unfolding** a cylinder **portrays** two circles attached to either side of the **rectangle**. The circles **symbolize** the top and bottom circular bases of the cylinder, and the **rectangle** represents the curved part of the cylinder.

### Other 3D Shapes

As a cylinder is a **3-dimensional** figure, there are many other 3-dimensional **shapes** used in geometry, named as:

- Cube
- Cuboid

**Pyramid**

- Cone
- Sphere

**Tetrahedron**

All the 3-dimensional geometric **figures** have specific **volumes** and surface areas according to their **geometric** structures. They have a number of **vertices**, edges, and faces.

For **example**, a cube consists of 6 facades and has a total of 12 **edges**, and 8 symmetrical vertices, whereas a **sphere** has 1 curved face, zero **edges**, and zero **vertices**. The net of all the 3-dimensional shapes can also be formed.

## Cylindrical Objects

Any **object** constituting a cylinder-like shape is said to be **cylindrical**. There are many cylindrical **objects** we see and use in our daily routine. The pencil **holder** we use for holding our **pens** and pencils is basically a **cylinder**. The **LPG** gas cylinder is cylindrical in shape.

The food cans or cold drink **cans** which we enjoy eating and drinking are examples of cylinders. **Buckets** and dustbins are also cylindrical in shape. The **trunk** and log of wood are also in the form of a **cylinder**. Candles, chimneys, **drums**, beakers, and test tubes are also examples of **objects** in a cylindrical shape.

## Practical Application of Geometrical Cylinders

**Cylinders** have a wide range of practical applications in **engineering** and **technology,** making them an **important** shape in the field. The most common uses for** cylindrical shapes **can be demonstrated as follows:

**Containers:**Cylinders are often used as containers for various products, such as**liquids**or**solids.**This is because they offer**efficient**use of space and can withstand stacking and**pressure.****Pipes: Cylinders**are also used in piping systems to transport liquids and gases, as they have a large interior**volume**and a small exterior surface**area.****Engine Design: Cylinders**play a key role in internal combustion engines. They are used to contain the**fuel**and**air mixture,**which is compressed and ignited to produce**power.****Pressure Vessels**: Cylinders are used as**pressure vessels**for storing compressed**gases, boilers,**and**heat exchangers.**They provide a strong and efficient structure to withstand high**pressures.****Bearings:**Cylinders are used as rollers and bearings in conveyor rollers, wheels, and gears. The**smooth cylindrical**surface offers low friction and wear**resistance,**making them ideal for**high-speed**and high-load applications.**Electrical Equipment:**Cylinders are also utilized in electrical equipment such as**transformers, inductors,**and**capacitors.**They help control electromagnetic fields.**Medical Devices: Cylinders**are used in medical devices such as**syringes,**catheters, and IV bags. The**cylindrical shape**is convenient and easy to use for**administering**fluids to patients.

Only a handful of **numerous practical** applications of cylindrical shapes were provided in the above topic in **engineering** and **technology.** Their versatility, combined with their strength and **efficiency,** make them an **essential** element in many **products** and **systems.**

## Solved Examples Involving Cylinders

### Example 1

A **cylindrical** bucket with a height of 30cm and a 15cm wide base radius is filled with sand. What will be the **total** surface area and **volume** of the bucket?

### Solution

Given data:

Height = h = 30cm

Base **radius **= r = 15 cm

Total surface area = A = ?

Volume = V = ?

First, we find the total **surface** area using the formula:

**Cylindrical surface area** = 2πr(h + r) square units

Putting the values of **radius** and height in the above formula:

A = 2 * 3.141 * 15(30 + 15)

= 2 * 3.141 * 15(45)

= 2 * 3.141 * 675

= 1350 * 3.141

= 4240 cm^{2}

Finding the **volume** of the bucket by using the formula:

**Volume** of cylindrical bucket= πhr^{2}

Putting the values of **radius** and height in the above **formula**:

V = 3.141 * 30 * (15)^{2}

**V = 20.925 cm ^{3}**.

Hence, the **cylindrical** bucket has a total surface area of 4240 cm^{2} and a **volume** of 20.925 cm^{3}.

### Example 2

What will be the **radius** of the cylinder whose volume is 550 cm^{3} and **height** of 5cm?

### Solution

Given data:

Height = h = 5cm

**Volume** = V = 550 cm^{3}

Radius = r = ?

Using the formula of **volume**, we can find the radius as:

Volume = V = πhr^{2} **cubic** units

r^{2} = V \ πh

r = √V \ πh

Putting the values of volume and **height** in the above formula:

r = √550 \ (3.141*5)

r = √550 \ 15.705

**r = 6 cm**

Hence, a **cylinder** with a volume of 550 cm^{3} and a height of 5 cm has a **radius **of 6 cm.

*All images were created with GeoGebra.*