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Why is the curved surface of cone not 2pi x r x l when the circumference is 2 x pi x r and L is the slant height that moves through this distance?
Wiki User
∙ 12y ago
Good question. Firstly, I'm assuming you are referring to a regular cone (i.e one with the same slope on all sides, as opposed to one where the uppermost "tip" is pushed off centre).
The area 2*pi*radius* length does give you a "surface", but it is based on the base measurements of the cone - it is the surface that would be created if you were to extend the curved surface straight upwards from the base of the cone (i.e creating a cylinder, not a cone).
A cone clearly has less curved surface area than a cylinder - in fact, it has half the surface area of the equivalent cylinder. So the equation is pi*radius*slant height. (i.e not 2*pi*radius*slant height).
Wiki User
∙ 12y ago
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