Surface Area of a Cylinder Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the surface area of a cylinder?
Answer
Surface area of a cylinder
S = 2 · π · r² + 2 · π · r · h
Here r is the radius, h is the height, perpendicular to the base. The result comes out in square units.
Where the formula comes from
S = 2 · π · r² + 2 · π · r · h
Unroll the can. The side becomes a rectangle whose width is the circumference 2πr and whose height is h; the two ends are discs of πr² each. Add them: 2πr² + 2πrh.
Worked examples
Let r = 3, h = 10. Then the surface area of a cylinder ≈ 245.04 square units.
Let r = 1.5, h = 2.4. Then the surface area of a cylinder ≈ 36.76 square units.
The common mistake
Counting one end instead of two, or none. An open pipe has only the 2πrh; a tin can has both discs. Decide what the object actually is before adding.
Other quantities: Cylinder
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See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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Values from the Formula (h = 10)
| If r = | Surface area |
|---|---|
| 1 | ≈ 69.12 square units |
| 2 | ≈ 150.8 square units |
| 3 | ≈ 245.04 square units |
| 4 | ≈ 351.86 square units |
| 5 | ≈ 471.24 square units |
| 10 | ≈ 1,256.64 square units |
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the surface area of a cylinder? (The answer is: S = 2 · π · r² + 2 · π · r · h). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter