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在复习立体几何有关旋转体的截面问题时,我向学生提出这样一个问题:“过圆柱、圆锥、圆台的母线的所有截面中轴截面面积是否一定最大?”很多学生认为“轴截面面积一定最大。”有的学生甚至觉得这样一个问题不值得一提。其实不然,圆柱的轴截面面积最大是无可非议的,但圆锥、圆台就不一定如此。例如,高为1而底面半径为3~(1/2)的圆锥的轴截面面积是
When reviewing the problem of the cross-section of the rotating body in the three-dimensional geometry, I asked the student the question: “Is the cross-sectional area of the shaft of all the cross-sections of the busbars, cones, and cones necessarily the largest?” Many students think that “the area of the shaft cross-section must be the largest Some students even think that such a problem is not worth mentioning. In actual fact, the largest cross-sectional area of the cylindrical shaft is unquestionable, but cones and circular tables are not necessarily the same. For example, the area of the axis of a cone whose height is 1 and the radius of the bottom surface is 3~(1/2) is