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众所周知,一个多面体切割成若干个小多面体后,这些小多面体的体积之和与原多面体的体积相等。运用这一思想方法,可以方便地解得一类关于已知多面体内一点与各面都有垂线段条件下的立几问题。仅举一例。一球外切一四棱台,求证二者体积之比等于二者表面积之比。证明连接球心和四棱台的各顶点,得到六个小四梭锥,其底面分别是S_1,S_2,…,S_6,球半径的R,于是根据体积相等关系得
It is known that after a polyhedron is cut into a number of small polyhedrons, the sum of the volume of these polyhedrons is equal to the volume of the original polyhedron. Using this method of thinking, one can easily solve a class of problems concerning the condition that a point in the polyhedron has a vertical line with each face. Just one example. A quadrangular table is cut out of the ball to verify that the ratio of the two volumes is equal to the ratio of the surface area of the two. Prove that connect the center of the sphere and the vertices of the quadrangular pyramid to obtain six small four-barrel cones whose bottom surfaces are S_1, S_2,..., S_6, respectively, and the radius of the sphere is R, so the relationship between the volumes is equal.