Surface Area of a Cylinder
Total surface area of a closed cylinder.
Formula
Variables
Example
Radius 2, height 5: A = 2π·2·(2+5) ≈ 87.9 square units.
How it works
This formula gives the total outside area of a closed cylinder, including both circular ends and the curved side. The two ends contribute 2c0r b2, and the curved surface becomes a rectangle when unrolled, with width 2c0r and height h, giving 2c0rh. Adding these parts together simplifies to 2c0r(r + h).
When to use it
Use this when you need the total material covering a cylinder, such as for cans, pipes with lids, drums, or water tanks. It is useful in geometry problems, packaging, manufacturing, and any situation asking for the full exterior surface area.
Worked example, step by step
Given: r = 3, h = 4 A = 2c0r(r + h) A = 2c0(3)(3 + 4) A = 2c0(3)(7) A = 42c0 A 131.9 square units
Common mistakes to avoid
- Forgetting to include both circular ends when the cylinder is closed
- Using the diameter instead of the radius in the formula
- Calculating only the curved surface area and leaving out the top and bottom
Did You Know?
Unroll a cylinder's side and it becomes a rectangle — that's where the 2πrh term comes from.
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