Two simple methods to calculate the ares and volume called improved square grid method and cube cutting method are proposed in this paper. For any plane curve or space surface satisfying certain conditions, by our method, the error of measurement is of the second infinitive order of measuring unit (the side length of the square grid or the side length of the little cube) when the unit is small enough. And when some properties of the curve or the surface can be found or its varying bounds can be evaluated, it is pointed out, in order to make the error smaller than any given value, how small the length of the measuring unit should be.
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