My Math Forum Calculating volume of hemisphere and surface area of hemisphere

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 October 28th, 2014, 10:06 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, 11:11 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 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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