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本刊去年第四期“疑难解析”一栏中,曾刊载《圆锥的轴截面是最大截面吗?》一文。文中就过圆锥顶点的截面的最大值的求法作了研究。但笔者认为文中介绍的最大值,求法过于复杂,在此想介绍一种较为简便的求法。如右图:设圆锥为VO,其底面半径为R,母线长为l,则分两种情况加以讨论。 (i)圆锥的轴截面的顶角不大于90°的情况。即k/l≤(2)~(1/2)/2 这时由于过顶点的截面中,顶角最大的是轴截面,所以S_(max)=1/2l~2sinθ(其中θ为轴截面的顶角),特别地方当θ=0°时,S_(max)=1/2l~2。
In the fourth issue of “Difficult Resolution” last year, the journal published the article “Axis Section of Cone Is Max Section?”. In this paper, the maximum value of the section of the cone vertex is studied. However, the author believes that the maximum value introduced in the article is too complicated to be solved. I would like to introduce a relatively simple method to solve this problem. As shown in the right figure: If the cone is VO, its bottom radius is R, and the bus length is l, it will be discussed in two cases. (i) The case where the apex angle of the shaft section of the cone is not more than 90°. That is, k/l ≤ (2) ~ (1/2)/2 At this point in the cross-section of the vertex, the apex angle has the largest axial section, so S_(max)=1/2l~2sinθ (where θ is the axial section The top corner), special place when θ = 0 °, S_ (max) = 1/2l ~ 2.