Volume⏱ 4 min read

Volume of a Cylinder

V = πr²h

What is the Volume of a Cylinder?

A cylinder has two circular faces connected by a curved surface. Its volume is the area of the circular base (πr²) multiplied by the height — essentially, stacking identical circles on top of each other until you reach the full height.

This "base area times height" pattern applies to any prism with a uniform cross-section, not just cylinders — it's a general principle in solid geometry, with the cylinder as the case where that cross-section is a circle.

What Each Variable Means

VolumeThe three-dimensional space inside the cylinder.

RadiusThe radius of the circular base.

HeightThe perpendicular height of the cylinder.

When to Use It

Finding the volume of any cylindrical container, like a can, pipe, or tank
Estimating how much liquid a cylindrical container can hold
As a comparison point for the volume of a cone with the same base and height

Step-by-Step Examples

Example 1: Finding a can's volume

Problem: A can has radius 3 cm and height 10 cm. What is its volume?

Identify the known values

Radius and height are both given.

r = 3 cm, h = 10 cm

Calculate r²

Square the radius first.

r² = 9 cm²

Apply the formula

Multiply by π and the height.

V = π × 9 × 10 = 90π

✓

Answer: V ≈ 282.74 cm³

Example 2: Finding a missing height

Problem: A cylindrical tank has a volume of 500π m³ and a radius of 5 m. Find its height.

Rearrange the formula

Solve V = πr²h for height.

h = V / (πr²)

Substitute and calculate

Divide the volume by π times the radius squared.

h = 500π / (π × 25) = 500/25

✓

Answer: h = 20 m

Interactive Calculator

r (radius)h (height)

Result will appear here

Solving for Other Variables

h = V / (πr²)Solve for height when volume and radius are known.

Common Mistakes

Mistake: Squaring the diameter instead of the radius.
Fix: The formula needs r², using the radius — if you're given the diameter, divide it by 2 first before squaring.
Mistake: Confusing the cylinder volume with the cone volume for the same base and height.
Fix: A cone with the same base and height has exactly one-third the cylinder's volume — don't forget the extra 1/3 factor when working with a cone instead.

Practice Questions

A cylinder has radius 4 cm and height 12 cm. Find its volume.
A cylindrical tank has volume 200π m³ and height 8 m. Find its radius.
Hint: Rearrange V = πr²h to solve for r, then take the square root.

Frequently Asked Questions

How is this related to the area of a circle?

The r² term is literally the circle area formula (A = πr²) applied to the cylinder's base — volume is that base area multiplied straight through by the height.

Does this formula work for an oblique (slanted) cylinder?

Yes, as long as h is measured as the perpendicular height between the two circular faces, not the slant length along the side.