Surface Area of a Cylinder
Calculate the total surface area of a cylinder including the top, bottom, and curved side.
Used in manufacturing and packaging.
The Formula
SA = 2πr² + 2πrh = 2πr(r + h)
The total surface area includes two circular ends and the rectangular side that wraps around. If you unroll the side, it forms a rectangle with width = circumference and height = h.
Variables
| Symbol | Meaning |
|---|---|
| SA | Total surface area |
| r | Radius of the circular base |
| h | Height of the cylinder |
| 2πr² | Area of the two circular ends |
| 2πrh | Area of the curved side (lateral surface) |
Example 1
A can has radius 4 cm and height 12 cm
SA = 2π(4)(4 + 12) = 2π(4)(16)
SA = 128π
SA ≈ 402.1 cm²
Example 2
A pipe is 2 m long with radius 0.05 m. Find the lateral surface only.
Lateral SA = 2πrh = 2π(0.05)(2)
Lateral SA = 0.2π
Lateral SA ≈ 0.628 m²
When to Use It
Use the cylinder surface area formula when:
- Calculating material needed for cans, tubes, or tanks
- Estimating paint or coating coverage for cylindrical objects
- Designing labels that wrap around cylindrical containers
- Computing heat transfer surfaces for pipes and boilers