Volume of a Cylinder

Introduction

Cylinders are everywhere, including water bottles, tanks, pipes, and cans. In geometry, a cylinder is a 3D shape with two circular bases and a curved surface that connects them. One of the most useful ideas about cylinders is how to find their volume and surface area. Whether you are working with real-life containers or solving math problems, knowing the formulas for the volume of a cylinder and its surface areas helps you achieve precise results. Let’s explore this important concept with simple explanations and clear formulas.

 

Table of Contents

• What is a Cylinder?
• Volume of Cylinder
• Formula of Volume of Cylinder
• Total Surface Area of Cylinder
• Curved Surface Area (CSA) of Cylinder
• Volume of Hollow Cylinder
• Units Used in Volume Calculation
• How to Convert Volume to Litres
• Real-life Applications
• Practice Questions
• Common Errors
• Tips & Tricks
• Fun Facts
• Conclusion
• FAQs on Volume of Cylinder

 

What is a Cylinder?

A cylinder is a three-dimensional shape with two identical circular bases and one curved surface. It looks like a tube or can and has height, radius, and diameter as its main parts.

 

Volume of Cylinder

The volume of a cylinder is the amount of space inside it. It tells us how much liquid or solid the cylinder can hold.

Think of filling a pipe with water the volume tells us how much it can carry.

 

Formula of Volume of Cylinder

The formula is:

Volume (V) = π × r² × h

Where:

• r = radius of the circular base

• h = height of the cylinder

• π = 3.141 (approximately)

If diameter (d) is given, remember:

r = d / 2

Example:

If radius = 4 cm and height = 10 cm,

V = π × 4² × 10 = 3.141 × 16 × 10 = 502.65 cm³

 

Total Surface Area of Cylinder

The total surface area of cylinder includes:

1. Curved (side) surface area

2. Area of both circular bases

TSA = 2πr(h + r)

Where:

• r = radius

• h = height

Example:

r = 5 cm, h = 10 cm

TSA = 2 × 3.141 × 5 × (10 + 5) = 471.2 cm²

 

Curved Surface Area (CSA) of Cylinder

The curved surface is only the side area without the top and bottom circles.

CSA = 2πrh

 

Volume of Hollow Cylinder

A hollow cylinder has two radii - outer and inner.

Volume = πh(R² − r²)

Where R = outer radius and r = inner radius.

 

Units Used in Volume Calculation

• cm³ (cubic centimeters)

• m³ (cubic meters)

• Litres (1 litre = 1000 cm³)
  Always keep your units consistent!
  
  

How to Convert Volume to Litres

Use this conversion:

1 litre = 1000 cm³

So, to convert:

Litres = Volume in cm³ ÷ 1000

Example:

Volume = 2000 cm³ → Litres = 2000 ÷ 1000 = 2 litres

 

Real-life Applications

• Measuring water in tanks

• Determining milk or oil in containers

• Designing pipes and tubes

• Calculating space in drums or barrels

• Understanding storage capacity in industries
  
  

Practice Questions

1. Find the volume of a cylinder with radius 7 cm and height 10 cm.

2. A cylinder has diameter 12 cm and height 20 cm. Find its volume.

3. Calculate TSA of a cylinder: radius = 6 cm, height = 9 cm.

4. A hollow cylinder has outer radius 10 cm, inner radius 7 cm, height 15 cm. Find volume.

5. Convert 2500 cm³ to litres.
   
   

Common Errors

• Forgetting to square the radius (r²)

• Mixing up diameter and radius

• Using wrong units

• Leaving π as a symbol in final answers

• Ignoring both ends when calculating total surface area
  
  

Tips & Tricks

• Always check if radius or diameter is given

• Use π = 3.141 or 22/7 depending on question

• Practice unit conversion regularly

• Use diagrams to visualize the problem

• Keep formulas on flashcards for quick revision
  
  

Fun Facts

• Pringles cans are a great example of a perfect cylinder!

• Cylinders have the most volume among solids with the same surface area.

• Fuel tanks and gas cylinders are designed using these formulas.

• Engineers use cylinder calculations for bridge pillars and pipelines.
  
  

Conclusion

Understanding the volume of a cylinder and its surface areas is important in both school and everyday tasks. Whether measuring liquids or designing containers, the formulas for the volume of a cylinder and its total surface area help solve practical problems easily. Learn to apply the formulas correctly, practice problems, and visualize the 3D shape. This makes learning enjoyable and useful.

 

Related Topics

Similar Triangles - Understand Similar Triangles with Easy Examples

Types of Triangles - Learn Types of Triangles with Clear Visual Guides

 

Frequently Asked Questions on Volume of Cylinder

1. What is the formula for volume of cylinders?

Ans: The volume of a cylinder is given by:

V = π × r² × h, where r is radius and h is height.

 

2. What is the TSA and CSA of cylinders?

Ans: 

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

• CSA (Curved Surface Area) = 2πrh
  
  

3. Why is the volume of cone 1/3 of cylinder?

Ans: A cone has the same base and height as a cylinder but only takes up 1/3 the space. So,

Volume of cone = (1/3) × π × r² × h

 

4. What is the formula for the volume of a cylinder tank?

Ans: The formula is the same:

V = π × r² × h

Just ensure you use correct units (litres or m³) depending on the tank's size.

 

5. How to calculate litres in a cylinder?

Ans:  First, find the volume in cm³ using the formula. Then convert to litres by dividing by 1000:

Litres = Volume in cm³ ÷ 1000

 

Learn more about  Volume of a Cylinder and explore engaging math concepts at The Orchids The International School.