Surface area of a cone
Maths and statistics discussion, revision, exam and homework help.
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Surface area of a coneI want to prove that the surface area of a cone of radius r and height h is
where l is the lateral height of the cone.
We take a ring of width
distance from its apex.
The surface area of the ring is
where y is the radius of the ring.
Using similar triangles,
therefore, surface area is 
Adding all of these rings together,
What am I doing wrong? -
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Re: Surface area of a coneIt's easier to consider its net.(Original post by r2enigma)
I want to prove that the surface area of a cone of radius r and height h is where l is the lateral height of the cone.
We take a ring of width distance from its apex.
The surface area of the ring is where y is the radius of the ring.
Using similar triangles, therefore, surface area is
Adding all of these rings together,
What am I doing wrong?
Are you required to use integration? -
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Re: Surface area of a coneYou've assumed that dx is an infinitesimal increase in x but it's not because x is the distance from the apex and dx is the distance along the cone's surface not the axis.(Original post by r2enigma)
I want to prove that the surface area of a cone of radius r and height h is where l is the lateral height of the cone.
We take a ring of width distance from its apex.
The surface area of the ring is where y is the radius of the ring.
Using similar triangles, therefore, surface area is
Adding all of these rings together,
What am I doing wrong? -
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Re: Surface area of a coneThis is wrong. A cone is made up of "rings" with sloping sides, and so their surface area is bigger than 2 pi y dx (which would be correct if the slides did NOT slope).(Original post by r2enigma)
I want to prove that the surface area of a cone of radius r and height h is where l is the lateral height of the cone.
We take a ring of width distance from its apex.
The surface area of the ring is where y is the radius of the ring.
[I think. It's not 100% clear what you're doing without diagrams].
