How it works
What "area of a cylinder" really means
The cylinder surface area problem combines three distinct shapes: the curved side (lateral) and two flat circular ends. "Surface area" in school maths almost always means total surface area — all three added together.
Some problems ask for just the lateral area (a label wrapped around a can, a paint job on a silo wall, a sticker for a pipe). Always re-read the question to check which is being asked for.
The three formulas on one line
- Lateral area (the curved side): L = 2πrh
- Base area (each circular end): B = πr²
- Total surface area: A = 2πr² + 2πrh = 2πr(r + h)
Three worked examples
1. Drinks can — r = 3.3 cm, h = 11.5 cm
Lateral: 2π × 3.3 × 11.5 ≈ 238.5 cm².
Bases: 2 × π × 3.3² ≈ 68.4 cm².
Total: ≈ 306.9 cm². The label on a 330 ml can covers only the lateral area — roughly 239 cm² of printable space.
2. Hot water cylinder — r = 0.25 m, h = 1.5 m
Insulation jackets wrap only the side, so you need lateral area: 2π × 0.25 × 1.5 ≈ 2.36 m². Plumbers add ~10% for overlap, so buy a 2.6 m² jacket.
3. Garden roller — r = 0.2 m, h = 0.6 m
Paint covers only the outside of the drum (lateral): 2π × 0.2 × 0.6 ≈ 0.754 m². At 10 m²/L coverage for exterior metal paint, you need ≈ 75 ml per coat.
Open vs closed cylinders
A closed cylinder (a sealed can) uses the full A = 2πr(r + h).
An open cylinder (a beaker, a planter with no lid) has only one base: A = 2πrh + πr² = πr(2h + r).
A tube (both ends open, e.g. a pipe section) is just the lateral area: A = 2πrh, unless the tube has measurable wall thickness, in which case you subtract the inner cylinder.
How this connects to volume and capacity
Surface area grows with the square of the size, but volume grows with the cube — which is why giant storage cylinders lose less heat per litre than small ones (lower surface-to-volume ratio).
If you need the inside capacity, use our **cylinder volume calculadora. For sphere and cone problems use sphere volume and cone volume**.
Common mistakes
- Forgetting to double the base area. A closed cylinder has two circles, not one.
- Using diameter instead of radius. The formula needs r = d/2.
- Mixing units — if h is in metres and r in centimetres, convert first. Our tool handles this automatically.
- Writing 2πr² when you mean (2πr) × r. Write as 2π × r × r to keep the order of operations clean.
Works well with
- **Cylinder volume calculadora** — pair with surface area for any real-world container.
- **Rectangle area** — same "find the formula, plug in, check units" workflow.
- **Pythagoras calculadora** — needed when you have slant heights in oblique cylinders.
- **Conversion calculadoras** — switch between cm, m, inches and feet before you substitute.
How we check the maths
Every geometry widget on the site has unit tests in `lib/calculadoras/*.test.ts` that cover known textbook values and edge cases (radius 0, height 0, huge numbers). Our editorial policy and corrections policy explain how we source and verify content. Calculations run entirely in your browser.