Surface Area of a Cylinder –

Surface area of a cylinder is tested on both Foundation and Higher papers across AQA, Edexcel and OCR. Understanding the net of a cylinder — two circles and a rectangle — is the key to remembering the formula and adapting it for open or partially open cylinders. This topic often appears alongside volume of a cylinder questions.

What Is the Surface Area of a Cylinder?

The surface area of a cylinder is the total area of all its outer faces. A closed cylinder has three surfaces: two identical circular ends and one curved surface that wraps around the side.

If you "unroll" the curved surface, it becomes a rectangle. The width of that rectangle equals the circumference of the circle (2pi r), and its height equals the height of the cylinder (h). This is why the curved surface area is 2pi rh.

An open cylinder (like a tin without a lid) is missing one or both circular ends. You must read the question carefully to determine how many circles to include in your calculation.

Key Formulas

Step-by-Step Method

1. Check whether you have the radius or the diameter. If given the diameter, halve it.
2. Calculate the area of the two circular ends: 2 pi r².
3. Calculate the curved surface area: 2 pi rh.
4. Add the results. If the cylinder is open-topped, use only one circle (pi r²) instead of two.

Worked Example 1 — Foundation Level

Question: A closed cylinder has radius 3 cm and height 10 cm. Find its total surface area to 1 decimal place.

Working: Two circles = 2 × pi × 3² = 2 × 9pi = 18pi Curved surface = 2 × pi × 3 × 10 = 60pi Total SA = 18pi + 60pi = 78pi = 245.044...

Answer: 245.0 cm² (1 d.p.)

Worked Example 2 — Higher Level

Question: An open-topped cylindrical container has radius 5 cm and height 14 cm. Find its total surface area to 3 significant figures.

Working: One circular base = pi × 5² = 25pi Curved surface = 2 × pi × 5 × 14 = 140pi Total SA = 25pi + 140pi = 165pi = 518.362...

Answer: 518 cm² (3 s.f.)

Worked Example 3 — Exam Style

Question: A cylindrical pipe is open at both ends. It has a diameter of 6 cm and a length of 20 cm. Find the total outer surface area of the pipe to 1 decimal place.

Working: Radius = 6 ÷ 2 = 3 cm No circular ends (open at both ends), so SA = curved surface area only. SA = 2 × pi × 3 × 20 = 120pi = 376.991...

Answer: 377.0 cm² (1 d.p.)

Common Mistakes

• Forgetting the circular ends. A closed cylinder has two circles. Write out each component separately so nothing is missed.
• Including circles when the cylinder is open. If the question says open-topped, include only one circle. If open at both ends, include no circles. Read the wording carefully.
• Using diameter instead of radius. All formulas use r. Halve the diameter if that is what the question provides.
• Confusing curved surface area with total surface area. The curved surface area (2 pi rh) does not include the circular ends. Total surface area adds the circles.

Exam Tips

• Sketch the net of the cylinder (two circles and a rectangle) alongside your working. This helps you visualise which faces to include and impresses the examiner.
• Remember: the rectangle width is the circumference (2pi r), not the diameter. This is the most common source of confusion.
• This formula is not given on the exam formula sheet — you must memorise it.
• Show each component (circles and curved surface) as separate lines of working. This earns method marks and makes errors easy to spot.
• Surface area questions often appear alongside volume questions — double-check which one the question is asking for by looking at the units (cm² for area, cm³ for volume).

Practice Questions

Q1 (Foundation): A closed cylinder has radius 4 cm and height 7 cm. Find its total surface area to the nearest whole number.

Q2 (Foundation): Find the curved surface area of a cylinder with radius 6 cm and height 9 cm. Give your answer to 1 decimal place.

Q3 (Higher): A closed cylinder has a total surface area of 200pi cm² and a radius of 5 cm. Find its height.

Practise surface area of a cylinder questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Surface Area
• Volume of a Cylinder
• Area of a Circle

Summary

• The total surface area of a closed cylinder is SA = 2 pi r² + 2 pi rh.
• The curved surface area alone is 2 pi rh — the area of the rectangle in the net.
• The rectangle in the net has width equal to the circumference (2 pi r) and height equal to h.
• For open cylinders, adjust the number of circular ends you include (0, 1, or 2).
• This formula is not on the exam formula sheet — you must learn it.
• Always check whether the question asks for total surface area or curved surface area only.