How to Find the Volume of a Cylinder – Formula & Examples
How to Find the Volume of a Cylinder – Radius, Diameter & Height
Cylinder volume is one of the clearest examples of the base-area principle: circular base area πr² multiplied by height.
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Cylinder Volume Formula
The circular base has area πr². A cylinder extends that same cross-section through height h, so volume is simply base area × height.
Step-by-Step Example
r=5 cm, h=12 cm:
Keep π until the final numerical step for better accuracy.
Cylinder Volume from Diameter
If diameter d is given, first find radius r=d/2, or substitute directly:
Example: diameter 10 cm, height 12 cm gives the same 300π cm³ result.
Find Height or Radius from Volume
Rearrange the same formula:
These reverse forms are useful when capacity/volume is known but one cylinder dimension is missing.
Worked Examples
r=3 m, h=8 m
d=14 in, h=20 in
r=7 in.
V=1000 cm³, r=4 cm — find h
Cylinder Volume vs Surface Area
Volume uses V=πr²h. Total surface area uses:
The first formula measures space inside; the second measures outside covering. Their units are cubic and square respectively.
Practice
r=2.5 m, h=6 m
Answer: V=π×6.25×6=37.5π≈117.81 m³.
d=8 cm, h=15 cm
r=4. V=π×16×15=240π≈753.98 cm³.
Questions People Ask
Open any question for a detailed explanation, not just a one-line answer.
How do you find the volume of a cylinder?
Use V=πr²h. Calculate the circular base area πr², then multiply by the perpendicular height.
How do I calculate cylinder volume from diameter?
Divide diameter by 2 to get radius, then use V=πr²h. Equivalently, use V=πd²h/4.
Why is radius squared?
The base is a circle whose area is πr². The cylinder volume extends that base area through the height.
How do I find cylinder height from volume?
Rearrange the formula to h=V/(πr²).
How do I find radius from cylinder volume?
Rearrange to r=√(V/(πh)).
What units should cylinder volume use?
Cubic units such as cm³, m³ or ft³ because three-dimensional space is being measured.
Is cylinder capacity the same as geometric volume?
For an ideal empty cylinder, geometric internal volume can represent capacity. Real vessels may have wall thickness, heads, fittings or unusable space that require more detailed modeling.
Where can I calculate cylinder volume automatically?
Use the Volume Calculator for cylinder volume and related surface-area results.
Related CalcTypes Resources
Methodology
This guide derives cylinder volume from circular base area and treats diameter and reverse problems as algebraic forms of the same relationship.