📘 Volume of Cylinder – Formula, Examples & Applications

When you look at a can of soda, a gas cylinder, or even a water pipe, you’re actually looking at a cylinder—a three-dimensional geometric shape. In mathematics, calculating the volume of a cylinder is a key concept taught from Class 8 onwards because it’s used in everyday scenarios and higher studies in geometry, physics, and engineering.

🔍 What is a Cylinder?

A cylinder is a 3D solid with two parallel circular bases and one curved surface connecting them. It looks like a tube or a pipe. The distance between the two bases is called the height (h), and the radius of the base is r.

📐 Volume of Cylinder Formula

The standard formula to find the volume of a cylinder is:

Volume = π × r² × h

Where:

π (pi) ≈ 3.14159
r = radius of the circular base
h = height of the cylinder

This formula gives the volume in cubic units (like cm³, m³, or in³), which tells you how much space is inside the cylinder.

✏️ Example Calculation

Let’s calculate the volume of a cylinder with:

Radius (r) = 5 cm
Height (h) = 10 cm

Using the formula:
Volume = π × 5² × 10 = π × 25 × 10 = 250π ≈ 785.4 cm³

So, the volume of the cylinder is 785.4 cubic centimeters.

🧠 Why Understanding Volume of Cylinder is Important

Knowing how to calculate the volume of cylinder is essential for:

Solving real-world problems (e.g., how much liquid a tank can hold)
Academic exams in maths and science
Engineering design and architecture
Everyday tasks like measuring container capacity

📊 Units of Volume

Depending on the size and context, the volume of a cylinder may be measured in:

Cubic centimeters (cm³)
Cubic meters (m³)
Liters (L) — 1,000 cm³ = 1 L
Cubic inches (in³)
Gallons (in US customary system)

📎 Tips to Remember

Always square the radius before multiplying by height.
Keep units consistent throughout the calculation.
Use π = 22/7 if the question instructs, or π = 3.14 for quick estimations.
Don’t forget to include units in your final answer.

🧪 Applications in Real Life

The volume of cylinder is used in:

Calculating capacity of water tanks and pipes
Designing fuel tanks and storage drums
Manufacturing cans, containers, and tubes
Understanding chemical volume in test tubes and cylinders

💡 Practice Questions

Find the volume of a cylinder with r = 7 cm and h = 14 cm.
A cylindrical tank has a radius of 2 meters and height of 5 meters. What is its volume in liters?
If the volume of a cylinder is 314 cm³ and the height is 4 cm, find the radius.

🧮 Volume of Hollow Cylinder

If you’re dealing with a hollow cylinder (like a pipe), the volume is:

Volume = π × h × (R² − r²)