论文部分内容阅读
大家知道:分别以直角三角形的斜边、两直角边所在直线为轴,旋转这个直角三角形所得的三个旋转体的体积为V、V_1、V_2,则 1/V~2=1/V_1~2+1/V_2~2·这是高中《立体几何》(甲种本)P_(146)第13题的结论.用它来解1988年高考第四题是件有趣的事: 如下图,正三棱锥S-ABC的侧面是边长为α的正三角形,D是S.4的中点,E是BC的中点,求△SDE绕直线SE旋转一周所得到的旋转体的体积(一九八八年全国高考理工类第四大题)。
Everyone knows: The volume of the three rotating bodies obtained by rotating this right-angled triangle is the V, V_1, and V_2, respectively, with the hypotenuse of a right-angled triangle and the straight line of two right-angled sides as the axis. Then 1/V~2=1/V_1~2. +1/V_2~2· This is the conclusion of the 13th problem of the high school “Three-Dimensional Geometry” (A type) P_ (146). It is interesting to use it to solve the fourth problem of the 1988 college entrance examination: The side of S-ABC is a regular triangle with side length α, D is the midpoint of S.4, E is the midpoint of BC, and the volume of the rotator obtained by rotating ΔSDE around line SE is calculated (1988). The fourth major title of the national college entrance examination science and technology class).