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Surface Area of Cylinder
A cylinder has two circular bases and one curved surface — together, they give us the total surface area of a cylinder.
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What is the Surface Area of a Cylinder?
Imagine cutting along the height of a soup can and flattening it out. What shape do you get? What are its dimensions?
The surface area of a cylinder refers to the total area that the cylinder's curved surface and circular bases cover. In other words: it is the total area covered by its two circular bases and its curved lateral surface.
The surface area of cylinder splits naturally into two pieces:
- Total Surface Area (TSA) — both circular bases plus the curved face. This is what you'd need if you were sealing every face of the cylinder.
- Curved Surface Area (CSA) — only the curved lateral surface. This is the area of the "label" wrapped around the side.
A cylinder has r = 5 cm and h = 12 cm. When calculating the surface area of cylinder, which part — TSA or CSA — would a label manufacturer care about?
Surface Area of a Cylinder Formula
There are two surface area of cylinder formulas to know — choose based on whether you need the full surface or just the curved side.
Curved Surface Area of Cylinder (CSA)
The curved surface area (CSA) of a cylinder is the surface area covered by its curved surface only. If the radius of the base of the cylinder is 'r' and the height of the cylinder is 'h', the curved surface area of a cylinder is calculated using the following formula:
Where:
r = radius of the cylinder
h = height of cylinder
π = 22/7 or 3.14
Imagine cutting the cylinder vertically along its height and unrolling it — the curved face of the surface area of cylinder becomes a rectangle of width 2πr (the circumference) and height h, giving CSA of cylinder = 2πr × h.
Example: Find the curved surface area of a cylinder of radius 7 cm and height 14 cm.
Using the formula CSA = 2πrh, substituting r = 7, h = 14:
CSA = 2 × 3.14 × 7 × 14 = 615.8 cm²
Total Surface Area of Cylinder (TSA)
The total surface area of the cylinder (TSA of cylinder) is obtained by adding the area of the two bases and the area of the curved surface. Consider a cylinder whose base has a radius 'r' and height of the cylinder is 'h'.
The total surface is two circular bases (each with area πr²) plus the curved face (2πrh). Adding them: 2πr² + 2πrh = 2πr(r + h).
Worked example
r = 5 in, h = 15 in:
TSA = 2π(5)(5 + 15) = 2π × 5 × 20 = 200π ≈ 628 sq in
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Practice
Five questions, increasing difficulty. Hints available — but try without them first.
Downloadable Worksheets
Question Set 1
Foundational Mensuration problems covering CSA, TSA, and volume of cylinders, cones, and spheres.
Download PDFQuestion Set 2
JEE-style Mensuration problems including melted-and-reformed solids, ratio problems, and frustums.
Download PDFKey Takeaways
FAQs on Surface Area of Cylinder
What is the surface area of a cylinder?
The surface area of a cylinder refers to the total area that the cylinder's curved surface and circular bases cover. It is measured in square units and computed using the formula 2πr(r + h), where r is the radius and h is the height.
What is the difference between TSA and CSA of a cylinder?
TSA (Total Surface Area) includes both the circular bases and the curved lateral face — formula 2πr(r + h). CSA (Curved Surface Area) is only the curved lateral face — formula 2πrh. Use CSA when you only care about the "label" area; use TSA when you need every face, including the top and bottom discs.
How do you find surface area when the diameter is given?
Halve the diameter to get the radius (r = d/2), then plug r into the standard formula 2πr(r + h). For example, if d = 14 cm and h = 10 cm, then r = 7 cm, and TSA = 2π(7)(7 + 10) = 238π cm².
What is the surface area of an open cylinder?
For a cylinder open at one end (one base missing), the surface area is πr² + 2πrh, which factors as πr(r + 2h). This applies to objects like open buckets, paper cups, and topless tanks.
Why does the curved surface area formula use 2πr × h?
If you cut the cylinder along its height and unroll the curved face, you get a rectangle. Its width equals the circumference of the base (2πr), and its height is just h. So the area is width × height = 2πr × h.
Can the curved surface area be zero?
Only if r = 0 or h = 0 — both of which make the cylinder degenerate. If r = 0, the cylinder collapses to a line. If h = 0, it collapses to a flat disc. Neither is a real cylinder, so for any genuine cylinder CSA is strictly positive.
What are common mistakes when calculating cylinder surface area?
The three biggest ones: (1) forgetting to double the base area — TSA uses 2πr², not πr², because there are two bases; (2) using diameter instead of radius — always halve the diameter first; (3) confusing CSA and TSA — re-read the problem and check whether the question is about a label (CSA) or the whole shell (TSA).
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