Formula sheet
Surface area of cylinder
2πr² + 2πrh is given on the exam formula sheet, it is the total surface area of a closed cylinder. You must still know the 2πr² is the two circular ends and 2πrh is the curved side, and drop a term if an end is open.
What the symbols mean
- r Radius of the circular end (length unit).
- h Height (length) of the cylinder (length unit).
- π Pi ≈ 3.142 or 22/7.
Given in the exam, or memorise?
2πr² + 2πrh is given on the exam formula sheet, it is the total surface area of a closed cylinder. You must still know the 2πr² is the two circular ends and 2πrh is the curved side, and drop a term if an end is open.
Why it works
Unroll a cylinder to see its flat parts.
- The two ends are circles, each of area πr², giving 2πr².
- Unrolling the curved side gives a rectangle of height h and width 2πr (the circumference).
- That rectangle has area 2πrh, so the total is 2πr² + 2πrh.
Worked example 1
Find the total surface area of a closed cylinder with radius 7 cm and height 10 cm. (Use π = 22/7)
- Surface area = 2πr² + 2πrh
- 2πr² = 2 × 22/7 × 7² = 2 × 154 = 308
- 2πrh = 2 × 22/7 × 7 × 10 = 440
- Total = 308 + 440 = 748
Worked example 2
A closed cylinder of radius 7 cm has total surface area 704 cm². Find its height.
(Use π = 22/7)
- Surface area = 2πr² + 2πrh
- 2πr² = 2 × 22/7 × 49 = 308
- 2πrh = 704 − 308 = 396
- 2 × 22/7 × 7 × h = 44h = 396
- h = 396 ÷ 44 = 9
Where students go wrong
- Leaving out the two circular ends (2πr²) when the cylinder is closed.
- Using diameter instead of radius in either term.
- Computing only the curved surface 2πrh when total surface area is asked.
- Giving the answer in cm instead of cm².
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
What is the difference between total and curved surface area?
Curved surface area is only the wraparound side, 2πrh. Total surface area of a closed cylinder adds the two flat circular ends, 2πr², giving 2πr² + 2πrh.
Read the question: a tin with a lid and base needs the full formula, while an open pipe uses only the curved part, or the curved part plus one end.
How do I handle an open cylinder like a pipe or cup?
Start from 2πr² + 2πrh and remove one πr² for each missing end. A cup open at the top has one end, so use πr² + 2πrh.
A pipe open at both ends has no circular ends, so use only 2πrh. Always picture the real object and count how many circular faces it truly has.
Is this cylinder formula on the SPM formula sheet?
Yes, 2πr² + 2πrh is printed, so you do not memorise it. Your marks come from applying it well: using the radius, squaring it in the first term, and deciding whether the object is closed or open.
Because it is given, spend effort on visualising the solid and choosing which terms to keep.