Volume of a cone
The volume of a cone is one-third of the volume of a cylinder having the same base radius and height.
Practice This ConceptMain explanation
Teacher explanation
A cone narrows to a point, so it holds less space than a cylinder with the same circular base and height. In fact, three such cones fill one matching cylinder. That is why the cone volume formula has the factor one-third.
Example
For a cone with radius 7 cm and height 12 cm, volume = 1/3 πr²h = 1/3 × π × 49 × 12 = 196π cm³ = 616 cm³.
Simple analogy
Cone holds one-third of a same base cylinder.
Common confusion
Students often forget the one-third factor or use slant height instead of perpendicular height.
Exam tip
For cone volume, height must be perpendicular to the base, not the slant height.
Answer writing and exam use
1-mark use
Write the exact meaning of volume of a cone in one clean line.
2-mark use
Define volume of a cone and add one example or condition.
3-mark use
Explain volume of a cone, show the method or example, and mention the common mistake.
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