Volume of a Cylinder
Calculate the volume of a cylinder using V = πr²h.
Find how much a cylindrical container holds with worked examples.
The Formula
V = π × r² × h
The volume of a cylinder equals the area of its circular base times its height.
Think of it as stacking circles on top of each other.
Variables
| Symbol | Meaning |
|---|---|
| V | Volume of the cylinder |
| π | Pi, approximately 3.14159 |
| r | Radius of the circular base |
| h | Height of the cylinder |
Example 1
Find the volume of a cylinder with radius 4 cm and height 10 cm
V = π × r² × h = π × 4² × 10
V = π × 16 × 10 = π × 160
V ≈ 502.65 cm³
Example 2
A water tank is 2 m in diameter and 3 m tall. How many liters does it hold?
Diameter = 2 m, so radius = 1 m, height = 3 m
V = π × 1² × 3 = 3π
V ≈ 9.42 m³
V ≈ 9,420 liters (1 m³ = 1,000 liters)
When to Use It
Use the volume of a cylinder formula when:
- Calculating how much a can, pipe, or tank holds
- Finding the capacity of cylindrical containers
- Working with pipes, columns, or tubes in engineering
- Comparing volumes of different cylindrical objects