Cylinder volume and surface area
Measure a right circular cylinder’s volume and total exterior area.
Cylinder volume and surface area is one of 8 solids formulas in the geometry section of this library, and it is used at middle school · high school level.
Why cylinder volume and surface area works
The volume stacks circular layers, each covering π times the radius squared, all the way up the height. For the outside, slitting the curved wall and unrolling it produces a rectangle whose width is the distance around the circle and whose height is the cylinder's height, and the two flat ends are added on.
What each symbol means
$r$ is radius and $h$ is perpendicular height.
Cylinder volume and surface area: when it holds
$r,h\ge0$; total surface area includes both circular bases.
When it stops applying
The surface expression assumes an upright cylinder, so that the curved wall unrolls into a true rectangle. Lean it over and the unrolled shape has slanted edges and a longer boundary, although the volume expression still holds.
Cylinder volume and surface area: a worked example
For $r=2,h=5$, $V=20\pi$ and $S=28\pi$.
The mistake to avoid
What people do: Counting only one of the two circular ends in the surface area.
Why it goes wrong: A closed can has both a top and a bottom, so leaving one out drops a whole disk: for a radius of 2 that is 4π of missing surface.
Do this instead: Ask whether the object is really closed. A pipe or an open cup genuinely does have fewer ends to count.
Cylinder volume and surface area: step by step
- Name the unknown, and the unit the answer has to come out in.
- Match the symbols to your values. $r$ is radius and $h$ is perpendicular height.
- Check the conditions before substituting. $r,h\ge0$; total surface area includes both circular bases.
- Substitute, keep exact values to the last line, then test the sign, size, and unit against a rough estimate — the check that catches most geometry slips.
Where this formula fits
- Subject
- Geometry formulas — 30 entries in this library
- Topic
- Solids
- Level
- Middle school · High school
Formulas are easiest to keep when they sit inside a method rather than on a list. Use the links below to see where cylinder volume and surface area comes from, to check a calculation against a tool, and to practise it until you can recall it without looking.
- Geometry Calculator — check your substitution and the value it produces.
- Study geometry — the subject guide that explains the ideas these formulas compress.
- Geometry Practice — questions that make you retrieve the formula instead of recognising it.
- All 30 geometry formulas — the full grouped reference, or the complete formula library.
Questions about cylinder volume and surface area
Does the height mean the slanted length in a tilted cylinder?
No. The volume uses the perpendicular gap between the two circular ends, not the length of the tilted axis joining their centres.
How do I find the volume of a pipe?
Take π times the difference between the squared outer radius and the squared inner radius, then multiply by the length of the pipe.
Which matters more, doubling the radius or doubling the height?
The radius, by a long way. It is squared, so doubling it multiplies the volume by four while doubling the height only doubles it.
How do I turn the volume into litres?
Work the volume out in cubic centimetres and divide by 1000, since one litre is exactly 1000 cubic centimetres.