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Surface of a spherical cap 
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#1
Jul2414, 12:45 AM

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from wiki:
even slice 1 has surface 62.8 (2\pi *10*1)? and its a (r_{1}) =4.36? so, the area of slice 4 (like all others) is 2pi*10*42pi*10*3 = 2pi*10= 62.8 is this correct? If it is not, what is the formula to find the area and a (r_{1}) of slice 1? Thanks 


#2
Jul2414, 03:22 AM

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It is possible to cut the horizontal slices so that each has the same surface area by varying the spacing.
To work out the surface area of each slice  use calculus. 


#3
Jul2414, 03:59 AM

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If I understood what you said, if we cut 10 equal slices of 1 cm , they will not have the same surface? Could you show me how to frame the equation(s)? Thanks 


#4
Jul2414, 04:08 AM

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Surface of a spherical cap
That's right  I would be surprised if the areas came out the same.
If we say that the floor is the xy plane and up is the +z axis, then you start by dividing the whole hemisphere (radius R) into very thin disks  thickness "dz". Then you want to work out the equation for the surface area "dS" of the disk between z and z+dz in terms of z and R. 


#5
Jul2414, 04:25 AM

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and the same happens all the way to the top to S_{1} Wher did I go wrong? 


#6
Jul2414, 04:38 AM

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Hah  I just tried it out and I am surprised ;)  try of for 2 slices.
I still think your best proof involves doing the calculus. 


#7
Jul2414, 05:12 AM

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If you are intrigued, check by calculus, and let me know! 


#8
Jul2414, 07:15 AM

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#9
Jul2414, 08:18 AM

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Yes. This is one of the reasons I like to answer questions here  sometimes someone surprises me.
This is the sort of thing that is obvious in retrospect. 


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