Explanation
Cylinder measurements
Find a right circular cylinder’s volume, total exterior surface including both end disks, or only its curved side surface. Enter radius and the perpendicular distance between the circular ends in metres.
V = πr²h
| r | Radius (m) |
|---|---|
| h | Height (m) |
Volume with radius 2 m and height 3 m
| Radius | 2 |
|---|---|
| Height | 3 |
| Result | 37.7 m³ |
V = πr²h = π × (2 m)² × 3 m = 37.6991118431 m³
S = 2πr(r + h)
| r | Radius (m) |
|---|---|
| h | Height (m) |
Total surface with radius 2 m and height 3 m
| Radius | 2 |
|---|---|
| Height | 3 |
| Result | 62.83 m² |
S = 2πr(r + h) = 2π × 2 m × (2 m + 3 m) = 62.8318530718 m²
L = 2πrh
| r | Radius (m) |
|---|---|
| h | Height (m) |
Curved surface with radius 2 m and height 3 m
| Radius | 2 |
|---|---|
| Height | 3 |
| Result | 37.7 m² |
L = 2πrh = 2π × 2 m × 3 m = 37.6991118431 m²
Diagram of this result
The cylinder is drawn in the proportions you entered, with the radius across the top and the height on a dimension line. Shading marks the volume, the whole outer surface, or only the curved side.
The cylinder is drawn in the proportions you entered, with the radius across the top and the height on a dimension line. Shading marks the volume, the whole outer surface, or only the curved side.
Common mistakes
Total surface adds the two circular ends to the curved side. An open container has a different surface; choose curved surface when excluding both ends. A slanted cylinder does not meet the assumptions of this surface formula.
Assumptions and limits
The cylinder is right circular, with positive radius and perpendicular height. Volume πr²h, total surface 2πr(r+h), and curved surface 2πrh all use finite-precision π and are labelled approximate. No material thickness or wastage is included. Canonical inputs are limited to 30 significant digits, 256 characters and adjusted exponent magnitude 100. Computation uses 50 significant digits without intermediate presentation rounding; output overflow fails explicitly. Approximate fixtures use absolute tolerance 1e-12 plus relative tolerance 1e-12.
How do the three measurements relate?
For radius 2 m and height 3 m, volume is 12π m³, curved surface is 12π m² and total surface is 20π m². The extra 8π m² accounts for both end disks.
Sources
Standard Euclidean measurement formulas: OpenStax Prealgebra 2e, measurement and geometry topics, https://openstax.org/details/books/prealgebra-2e. Worked examples use independent geometric identities.