Curved surface area of a cone
The curved surface area of a cone is the area of its sloping side, excluding the circular base.
Practice This ConceptMain explanation
Teacher explanation
A cone has one circular base and one curved sloping face. The sloping face is not measured by height; it is measured by the slant height. That is why the curved surface area uses radius and slant height, not the perpendicular height.
Example
For a cone with radius 5 cm and slant height 13 cm, CSA = πrl = π × 5 × 13 = 65π cm².
Simple analogy
Cone side means slant height, not vertical height.
Common confusion
Students often use the vertical height instead of the slant height in the formula.
Exam tip
If only the side of the cone is covered, use πrl and remember that l means slant height.
Answer writing and exam use
1-mark use
Write the exact meaning of curved surface area of a cone in one clean line.
2-mark use
Define curved surface area of a cone and add one example or condition.
3-mark use
Explain curved surface area of a cone, show the method or example, and mention the common mistake.
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