Closed cylinder: radius 2 cm, height 5 cm.
- Two circles: 2π(2²) = 8π cm².
- Lateral area: 2π(2)(5) = 20π cm².
- SA = 28π cm² ≈ 87.96 cm².
Surface area of cylinders
Unroll a curved surface into a rectangle.
The curved surface unwraps
Connect the circumference of a circular base to the lateral area and calculate cylinder surface area.
A cylinder’s lateral surface unwraps to a rectangle with width 2πr and height h, giving lateral area 2πrh.
Explore the dimensions
Predict first, then change one dimension. Diagrams are schematic; results use the entered values. Rounded values are marked ≈.
Add the circular ends
For a closed cylinder, SA = 2πr² + 2πrh. An open cylinder might have one base, both bases, or neither; read the context.
Radius is half the diameter
If a diameter is given, divide it by two before using r. Retain π until rounding at the end.
Worked examples
The same cylinder has no top.
- Subtract one circular base, 4π cm².
- Open surface area = 24π cm² ≈ 75.40 cm².
Guided Practice
A cylinder has radius 3 cm and height 4 cm. Find the lateral area in terms of π.
A first hint
Circumference × height.
Compare your reasoning
2π(3)(4) = 24π cm².
Practice
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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Connections
Explain why two cylinders can have the same volume but different surface areas.
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