Total surface area of a cylinder
The total surface area of a cylinder is the area of its curved surface plus the areas of both circular bases.
Practice This ConceptMain explanation
Teacher explanation
A closed cylinder has three exposed parts: one curved side and two circular ends. When a question asks for the outer or total surface area, all these exposed parts must be counted together. This is why the formula combines the curved part and the two bases into one expression.
Example
For a closed cylinder with radius 3 cm and height 8 cm, TSA = 2πr(h+r) = 2π × 3 × (8+3) = 66π cm², which is 207.43 cm² approximately.
Simple analogy
Total means side plus both ends.
Common confusion
Students often forget one or both circular bases and write only the curved surface area.
Exam tip
When the cylinder is closed or all outer surfaces are mentioned, use 2πr(h+r).
Answer writing and exam use
1-mark use
Write the exact meaning of total surface area of a cylinder in one clean line.
2-mark use
Define total surface area of a cylinder and add one example or condition.
3-mark use
Explain total surface area of a cylinder, show the method or example, and mention the common mistake.
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