Sheet № 106 · Foundation + Higher · AQA · Edexcel · OCR
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.
§Key definitions
Question:
A closed cylinder has radius 3 cm and height 10 cm. Find its total surface area to 1 decimal place.
Answer:
245.0 cm² (1 d.p.)
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.
§Formulas to memorise
Total surface area (closed) = 2 pi r² + 2 pi rh
Curved surface area only = 2 pi rh
Two circles = 2 × pi × 3² = 2 × 9pi = 18pi
Curved surface = 2 × pi × 3 × 10 = 60pi
Total SA = 18pi + 60pi = 78pi = 245.044...
One circular base = pi × 5² = 25pi
Curved surface = 2 × pi × 5 × 14 = 140pi
Total SA = 25pi + 140pi = 165pi = 518.362...
Radius = 6 ÷ 2 = 3 cm
SA = 2 × pi × 3 × 20 = 120pi = 376.991...
Worked example
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...
⚠ 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).