Volume of a Cylinder
The volume of a cylinder.
Formula
Variables
Example
Radius 2, height 10: V = π·2²·10 ≈ 125.7 cubic units.
How it works
A cylinder’s volume tells you how much space is inside it, measured in cubic units. The formula works because the base of a cylinder is a circle, and the area of that circle is πr²; multiplying that base area by the cylinder’s height stacks those circular layers into the full 3D shape. In other words, it is like taking the area of one circular slice and extending it straight up through the height.
When to use it
Use this formula whenever you need the capacity or interior space of a cylindrical object, such as a can, pipe, tank, or glass. It is also used in geometry problems that involve right circular cylinders and in science or engineering calculations involving containers and materials.
Worked example, step by step
A cylinder has radius 4 cm and height 7 cm. V = πr²h V = π × 4² × 7 V = π × 16 × 7 V = 112π V ≈ 351.9 cm³
Common mistakes to avoid
- Using the diameter instead of the radius in the formula
- Forgetting to square the radius before multiplying by the height
- Leaving the answer in square units instead of cubic units
Did You Know?
A cylinder is just a stack of identical circles — its volume is the circle's area times the height.
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