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October 28th, 2014, 11:06 AM  #1 
Newbie Joined: Oct 2014 From: England Posts: 3 Thanks: 0  Calculating volume of hemisphere and surface area of hemisphere
When calculating the volume of a hemisphere, you can use discs of height dx and radius y. However, when calculating the surface area of a hemisphere you cannot use rings of height dx. Why is this?

October 28th, 2014, 12:11 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,511 Thanks: 2514 Math Focus: Mainly analysis and algebra 
That's a very good question. As I understand it, it's because the error in the Riemann sum doesn't tend to zero (quickly enough) as $x \to 0$. This will be because the error in volume is of order $(\delta x)^2$ which goes to zero quicker than $\delta x$ which is the order of the error in curve length. 

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area, calculating, hemisphere, surface, volume 
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