Volume of a Cylinder
Calculate cylinder volume using V = πr²h and lateral surface area using 2πrh.
Includes worked examples for tanks, pipes, cans, and cylindrical containers.
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
Key Notes
- Volume scales as r² — doubling the radius quadruples the volume for the same height; this is why a pipe twice as wide carries four times the flow, which explains why upgrading from a 1-inch to a 2-inch water pipe is so significant
- Cavalieri's principle applies: an oblique (tilted) cylinder has the same volume as a right cylinder with the same base area and height — only the perpendicular height matters, not the slant length
- Using diameter instead of radius is the most common error — if given a diameter d, compute r = d/2 first; using d directly in the formula inflates the answer by a factor of 4 (d² instead of r² = d²/4)
- Total surface area of a closed cylinder (including both circular ends) is SA = 2πrh + 2πr² — a pipe (open at both ends) uses only the lateral surface SA = 2πrh; distinguish which is needed for material estimation problems