Cylinder

Introduction to Cylinder  

A cylinder is a common three-dimensional shape in geometry. It has two parallel circular bases connected by a curved surface. You can find cylinder shapes in everyday objects like gas tanks, pipes, and cans. They are crucial in geometry, engineering, architecture, and design.  

To understand the properties of a cylinder, you need to know terms like the volume of a cylinder, surface area of a cylinder, curved surface area of a cylinder, total surface area of a cylinder, and the formula of a cylinder. This knowledge helps solve real-world problems related to capacity, area, and material needs.  

 

Table of Contents

• What is a Cylinder?
• Types of Cylinder
• Properties of Cylinder
• Formula of Cylinder
• Cylinder Shape in Real Life
• Comparison: Volume vs Surface Area of Cylinder
• Solved Examples on Cylinder
• Conclusion
• FAQs On Cylinder

 

What is a Cylinder?  

A cylinder is a solid 3D shape with two identical circular bases aligned one above the other, joined by a curved surface. The axis of the cylinder is the straight line connecting the centers of the two bases.  

The most commonly studied type is the right circular cylinder, where the axis is perpendicular to the bases. The shape is symmetrical around its central axis and has no vertices or edges.  

 

Types of Cylinders  

In geometry, not all cylinders are the same. They can appear or function differently depending on their shape or position. Below are the main types of cylinders students should know about.  

 

1. Right Circular Cylinder  

This is the most common and easily recognizable type of cylinder. In a right circular cylinder, the two circular bases sit directly on top of each other, and the sides (curved surface) rise straight up. The height is at a right angle (90 degrees) to the base. Examples include water bottles, gas cylinders, and drink cans.  

 

2. Oblique Cylinder  

An oblique cylinder appears tilted to one side. The circular bases remain parallel, but the sides slant instead of going straight up. Think of a can that has been pushed over. It still has the same base and top but does not stand upright. The volume is calculated like a right circular cylinder.  

 

3. Elliptic Cylinder  

In an elliptic cylinder, the base is not a perfect circle but shaped like an ellipse (a stretched circle). This type is less common in daily life but may appear in advanced mathematics, engineering, or architectural designs. The sides curve like those of other cylinders, but the base looks oval.  

 

4. Hollow Cylinder (Cylindrical Shell)  

A hollow cylinder has a hole in the middle, resembling a pipe or tube. It has two circular bases: an outer one and an inner one. The space between forms the wall of the hollow cylinder. To find the volume, we subtract the volume of the smaller inner cylinder from the larger outer one. Common examples include straws, metal pipes, and plumbing tubes.  

 

5. Open Cylinder  

An open cylinder has only the curved side, lacking both top and bottom. It looks like a rolled sheet forming a tube. This type is often used in models or structures where only the side surface matters, such as in specific machines or decorative columns.  

 

Properties of Cylinder  

Understanding the properties of a cylinder is crucial for recognizing how it behaves in physical and mathematical contexts.  

Important Properties of Cylinder:  

• Two congruent circular bases.  

• A curved surface connecting the bases.  

• Fixed height between the bases.  

• Symmetrical around its axis.  

• No corners or edges.  

• Can be classified as right or oblique based on the axis position.  

These properties make cylinders efficient for storing and transporting materials and fluids.  

 

Formula of Cylinder  

To calculate quantities like the volume of a cylinder or the surface area of a cylinder, we use specific formulas dependent on the radius (r) and height (h) of the cylinder.  

Common Formulas of Cylinder:  

Volume of a Cylinder:  

V = π r² h  

 

Curved Surface Area of Cylinder:  

CSA = 2π r h  

 

Total Surface Area of Cylinder:  

TSA = 2π r (r + h)  

 

Area of Cylinder (Circular Base):  

A = π r²  

Understanding and applying these formulas is essential for solving practical and academic problems.  

 

Volume of a Cylinder  

The volume of a cylinder refers to the space inside it. It indicates how much material a cylinder can hold, measured in cubic units like cm³ or m³.  

 

Volume of a Cylinder Formula:  

Volume = π r² h  

 

Example:  

If a cylinder has a radius of 5 cm and a height of 10 cm:  

Volume = 3.1416 × (5)² × 10

             = 785.4 cm³  

The volume of a cylinder increases with the square of the radius and directly with the height.  

 

Curved Surface Area of Cylinder  

The curved surface area of a cylinder is the lateral area, excluding the bases. It wraps around the sides of the cylinder.  

Curved Surface Area Formula:  

CSA = 2π r h  

 

Example:  

If radius = 4 cm and height = 12 cm,  

CSA = 2 × 3.1416 × 4 × 12 = 301.59 cm²  

The curved surface area helps determine the material needed for side coverings.  

 

Total Surface Area of Cylinder  

The total surface area of a cylinder includes the curved surface plus the area of the two circular bases.  

Formula:  

Total surface area of cylinder = 2π r (r + h)  

 

Example:  

For a cylinder with radius = 3 cm and height = 7 cm:  

TSA = 2 × 3.1416 × 3 × (3 + 7) = 188.5 cm²  

The total surface area is needed when calculating the total area exposed to air or for packaging.  

 

Area of Cylinder  

The area of a cylinder can refer to:  

• The area of one circular base: π r²  

• The curved surface area of the cylinder  

• The total surface area of the cylinder 

Often, "area of cylinder" is used to refer to any of the above, but most commonly to the total surface area.  

Understanding the area of a cylinder is crucial in applications involving surface coverings or coatings.  

 

Cylinder Shape in Real Life  

The cylinder shape is found in these objects:  

• Gas cylinders  

• Cans and tins  

• Water tanks  

• Battery cells  

• Industrial pipes  

The cylinder shape is popular for its structural efficiency and symmetry. It evenly distributes pressure and maximizes storage. 

 

Comparison: Volume vs Surface Area of Cylinder

 

 

Each measurement is essential based on whether you're filling the cylinder, painting it, or wrapping it.

 

Solved Examples on Cylinder

Example 1: Find the Volume of a Cylinder

Question:
A Cylinder has a radius of 7 cm and a height of 10 cm. Find the volume of the Cylinder.

Solution:
We use the formula:
Volume of a Cylinder = π × r² × h

Here,
r = 7 cm
h = 10 cm

Volume = 3.1416 × 7 × 7 × 10
Volume = 3.1416 × 49 × 10
Volume = 3.1416 × 490
Volume = 1539.38 cm³

Answer: 1539.38 cubic centimeters

 

Example 2: Find the Curved Surface Area of a Cylinder

Question:
A Cylinder has a radius of 5 cm and height of 12 cm. Find the curved surface area of the Cylinder.

Solution:
Curved Surface Area (CSA) = 2 × π × r × h

Here,
r = 5 cm
h = 12 cm

CSA = 2 × 3.1416 × 5 × 12
CSA = 2 × 3.1416 × 60
CSA = 3.1416 × 120
CSA = 376.99 cm²

Answer: 376.99 square centimeters

 

Example 3: Find the Total Surface Area of a Cylinder

Question:
Find the total surface area of a Cylinder with radius 6 cm and height 8 cm.

Solution:
Total Surface Area (TSA) = 2 × π × r × (r + h)

Here,
r = 6 cm
h = 8 cm

TSA = 2 × 3.1416 × 6 × (6 + 8)
TSA = 2 × 3.1416 × 6 × 14
TSA = 3.1416 × 168
TSA = 527.79 cm²

Answer: 527.79 square centimeters

 

Example 4: Find the Area of Circular Base of a Cylinder

Question:
Find the area of the base of a Cylinder with radius 4 cm.

Solution:
Area of base = π × r²

Here,
r = 4 cm

Area = 3.1416 × 4 × 4
Area = 3.1416 × 16
Area = 50.27 cm²

Answer: 50.27 square centimeters

 

Example 5: If the Volume is Given, Find the Height of a Cylinder

Question:
The volume of a Cylinder is 785.4 cm³ and the radius is 5 cm. Find the height of the Cylinder.

Solution:
Volume = π × r² × h
785.4 = 3.1416 × 5 × 5 × h
785.4 = 3.1416 × 25 × h
785.4 = 78.54 × h

Now divide both sides by 78.54:
h = 785.4 ÷ 78.54
h = 10 cm

Answer: 10 cm

These examples show the application of the formula of Cylinder in real-world scenarios.

 

Conclusion  

The cylinder is a versatile geometric shape used in everyday life and various fields like design, manufacturing, and architecture. By understanding the formula for a cylinder and mastering calculations for the volume, surface area, curved surface area, and total surface area, you can efficiently solve both theoretical and practical problems.  

The cylinder shape is not only simple but also powerful in real-world applications. Learning about the properties of a cylinder gives students and professionals essential spatial and mathematical skills.  

 

Related Links

Volume of a Cylinder - Understand the concept and formula for finding the volume of a cylinder, with step-by-step examples to aid learning.

Volume of Cone - Learn how to calculate the volume of a cone using the standard formula, with visual illustrations and solved examples.

 

Frequently Asked Questions on Cylinder

1. What is the formula of a cylinder?

Ans:

• Curved Surface Area (CSA): 2πrh

• Total Surface Area (TSA): 2πr(h + r)

• Volume of a cylinder: πr²h
  Where r = radius, h = height
  
  

2. What is called a cylinder?

Ans: A cylinder is a 3D solid shape with two parallel circular bases connected by a curved surface. It resembles a can or a tube.

3. Does a cylinder have 2 or 3 faces?

Ans: A cylinder has 3 faces:

• 2 circular faces (top and bottom)

• 1 curved surface (side face)
  
  

4. What are the 7 properties of a cylinder?

Ans:

• Has two congruent circular bases

• Has a curved lateral surface

• Has a fixed height between the two bases

• Volume = πr²h

• Surface area = 2πr(h + r)

• No vertices (corners)

• No edges (sharp lines)

 

Learn all about cylinders with clear explanations and examples at Orchids The International School!