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对称是研究数学问题常用的思想方法 ,运用对称思想方法来研究旋转体的表面积问题 ,常可获得一些出人意料的、简捷明快的解法 .但有些问题的对称性并不那么直观 ,需要人为地添加构造 .例 1 如图 1 ,边长为 a的正六边形ABCDEF,以一边 AB所在的直线 l为轴旋转 ,求所得旋转体的表?
Symmetry is a commonly used method of thinking in the study of mathematics problems. Using symmetry methods to study the surface area of rotating bodies can often obtain unexpected and simple solutions. However, the symmetry of some problems is not so intuitive, and artificial structures need to be added. Example 1 As shown in Figure 1, the regular hexagon ABCDEF with a side length of a rotates on the straight line l on the side of AB to find the table of the resulting rotating body.