In the archaeological community there is an interest in knowing the volume of the vessels rescued in the excavations, to study, among other things, if the capacity measures were standardized. The problem is that sometimes it is not possible to check the volume physically because the piece is too delicate or too large or simply incomplete. There is a fairly widespread idea that it is sufficient to know a radial section of the vessel to reconstruct it in 3D. Then, the volume is approximated by dividing the height in small sub-intervals sufficiently small and in each sub-interval the volume is approximated by that of a cylinder. This is equivalent to using the composite rectangular rule for the squared radius. This method works well if the piece made around is regular, more specifically if the horizontal sections are circumferences. The point is that most archaeological pieces have deformations, which makes the previous method very inaccurate. In this work a method that, instead of using a single section, uses several radial sections equally spaced between 0 and $2\pi$ angles and then take the average, is proposed. It is shown that the method gives a volume approach of fourth order with respect to the angle. Numerical experiments are presented on an academic example whose horizontal sections are ellipses, another academic example with less symmetries and an example of a Pintia vessel with an evident deformation in which the proposed method is tested.

在考古界，人们有兴趣了解在开挖中救出的船只的数量，以研究容量度量是否标准化。问题在于，有时由于块太细小或太大或根本不完整而无法进行物理检查。有一个相当普遍的想法，即知道血管的径向截面以3D重建它就足够了。然后，通过将高度划分为足够小的小子间隔来近似体积，并且在每个子间隔中，用圆柱体近似体积。这等效于对平方半径使用复合矩形规则。如果周围制作的零件是规则的，则该方法效果很好，更具体地说，如果水平截面是圆周。关键是大多数考古作品都有变形，这使得以前的方法非常不准确。在这项工作中，一种方法不是使用单个截面，而是使用在0和$2\pi$提出角度，然后取平均值。结果表明，该方法相对于角度给出了四阶的体积逼近。在一个水平截面为椭圆形的学术实例，另一个对称性较小的学术实例以及具有明显变形的Pintia容器实例的数值实例上进行了数值实验，在其中测试了所提出的方法。