Curved surface area of a cylinder
The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases.
Practice This ConceptMain explanation
Teacher explanation
A cylinder looks like a rolled rectangle with two circular ends. If you cut the curved side and open it, it becomes a rectangle whose length is the circumference of the base and whose breadth is the height of the cylinder. That is why the curved surface area depends on radius and height, not on the base area.
Example
A tin can with radius 7 cm and height 10 cm needs side covering only. The area needed is 2πrh = 2 × π × 7 × 10 = 140π cm², which is 440 cm² when π = 22/7.
Simple analogy
Curved side only: 2πrh.
Common confusion
Students often use the total surface area formula and include the two circular ends even when only the side is required.
Exam tip
If the question says only the side, label, cover, or curved part, use 2πrh and do not add the bases.
Answer writing and exam use
1-mark use
Write the exact meaning of curved surface area of a cylinder in one clean line.
2-mark use
Define curved surface area of a cylinder and add one example or condition.
3-mark use
Explain curved surface area of a cylinder, show the method or example, and mention the common mistake.
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