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Recently after playing hours of Minecraft (and generating block volumes), a question popped up in my head: Is it possible to easily (by hand in a reasonable amount of time) determine the surface area of an arbitrary function? For instance, if you were to take the function $y=x^2$, and move it onto a graph with discrete coordinate values (with non-integer function values being rounded accordingly - something like $\text{Int}(y)=x^2$ for $[\text{Int}(a),\text{Int}(b)]$ ? Extending that further, like here would it be possible to find the volume of some equation or solid of revolution and in addition the surface area? In other words, could you calculate the area of a function using the rectangle method with midpoint approximation and equal width rectangles?

If these are not possible, can one find some sort of approximation of this area/volume more accurate than that of the integral it seems to represent? Thanks.

Community
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hedgepig
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I would propose using the rectangle method described here: http://en.wikipedia.org/wiki/Rectangle_method

The only problem is I'm not sure what to input for N given a generic volume. Maybe someone else can elaborate on this.

WafflesTasty
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  • Welcome to MSE! This is better left as a comment, although you do not yet have enough reputation for that. Regards – Amzoti Apr 04 '13 at 02:13
  • Oh, allright, I guess that's because it's not a complete answer? I hadn't even thought of it so thanks for the advice. – WafflesTasty Apr 04 '13 at 19:05
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    It would help if you could provide more details on the Rectangle Method and how it would apply. Also, you are correct as it is not complete. I am not the police, just trying to comment on why there were no up-votes and making recommendations. Regards – Amzoti Apr 04 '13 at 19:09