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I am trying to find the surface area of a 'biconcave disc', which is the shape of a red blood cell. I know the formula/length for the curve, which I am integrating to find the volume of the shape. To find the surface area of the shape, can I just multiply this length by $2 \pi$?

Following is the shape and curve I am talking about, with the first part showing a cross section of the 3D object, and the second showing the curve I am talking about.

A biconcave disc

I basically took the second curve and integrated it around the x-axis to find the volume.

achille hui
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kay
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    It is not clear at all what you mean by "formula/length for the curve". You have a three-dimensional object with volume; what curve are you looking at? Perhaps it would be better if you would show everything that you are doing to find the volume; that might at least clarify what it is you intend to multiply by $2\pi$. – David K Aug 08 '15 at 03:54
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    Look at the Area formula in wiki's entry of Surface of revolution. – achille hui Aug 08 '15 at 04:26
  • Your curve on the right is not the cross-section of the figure on the left! – user21820 Aug 08 '15 at 11:12

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You cannot. This follows already from the fact that it scales incorrectly – if you scale the whole thing up by $\lambda$, that quantity would scale with $\lambda$ whereas it should scale with $\lambda^2$.

Each curve element sweeps a surface area element of different radius. The correct way to take this into account is given in the Wikipedia article that achille hui linked to in a comment.

joriki
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