Case 1
- Base radius
- 3
- Height
- 5
150.796447
Open with these valuesCylinder Surface Area Calculator
150.796447units²
Result: 150.796447 units²Both ends plus the wall: 2πr² + 2πrh, which factors to 2πr(r + h). For an open tube or a label that only wraps the side, use the wall alone — 2πrh, which is 2πrh and nothing more.
The numbers at a glance
Held fixed: Base radius 3.000.
| Height | Result |
|---|---|
| 2.000 | 94.247780 |
| 4.000 | 131.946891 |
| 5.000Your value | 150.796447 |
| 6.000 | 169.646003 |
| 8.000 | 207.345115 |
| 10.000 | 245.044227 |
Worked examples
Case 2
- Base radius
- 1
- Height
- 1
12.566371
Open with these valuesCase 3
- Base radius
- 5
- Height
- 10
471.238898
Open with these valuesHow it's calculated
A = 2 × π × r × (r + h)
- StepMeasure the radius of the circular end.
- StepMeasure the height between the two ends.
- ResultRead the total area in the square of the unit you entered.
Reference table
| Radius, height | Exact | Total area |
|---|---|---|
| 0.5, 3 | 3.5π | 10.995574 |
| 1, 1 | 4π | 12.566371 |
| 2, 7 | 36π | 113.097336 |
| 3, 5 | 48π | 150.796447 |
| 4, 4 | 64π | 201.061930 |
| 5, 10 | 150π | 471.238898 |
Questions
How do you find the surface area of a cylinder?
Add the two circular ends, 2πr², to the wall, 2πrh. Radius 3 and height 5 give 48π, about 150.80 square units.
How big is the label on a tin?
The wall only: 2πrh. A tin of radius 3 and height 5 needs a label 2π × 3 = 18.85 wide and 5 tall, about 94.25 square units.
What about a tube open at both ends?
Then neither circle counts and the area is just 2πrh. Open at one end, add a single πr².
Which shape uses the least material for a given volume?
For a closed cylinder, the one whose height equals its diameter — height twice the radius. That is why the case 4, 4 above is not the cheapest: it is taller than wide.
Sources and last check
Information, not professional advice.