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October 28th, 2014, 11:06 AM   #1
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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?
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October 28th, 2014, 12:11 PM   #2
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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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