Cylinders: Surface Area
Two circles plus the curved face.
Key idea
Two circles plus the curved face.
In depth
Unrolled, the curved surface is a rectangle with width 2πr (the circumference) and height h. Add two circular ends: SA = 2πrh + 2πr².
Worked example
r = 2, h = 5: 2π(2)(5) + 2π(4) = 20π + 8π = 28π ≈ 87.96.
Formula
Real-world uses
- Calculating the metal needed for a drinks can or the label for a jar
Common mistake
Leaving out the two circular ends.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Cylinders: Surface Area?
Two circles plus the curved face. It is a topic at the intermediate level in Geometry.
What is the formula for Cylinders: Surface Area?
The key formula is SA = 2πr² + 2πrh.
Where is Cylinders: Surface Area used in real life?
Real-world examples: Calculating the metal needed for a drinks can or the label for a jar.
What should I learn before Cylinders: Surface Area?
Make sure you are comfortable with Surface Area of Prisms, the previous topic in Geometry.
What is a common mistake with Cylinders: Surface Area?
Leaving out the two circular ends.
How can I practise Cylinders: Surface Area?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Cylinders: Surface Area?
Move on to Cones next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.