利用祖晅原理求球体积时,要设计辅助体。课本《立体几何》中,设计的是一个底面半径与高相等的圆柱,中间挖去一个倒置圆锥所得的几何体。除此辅助体外,还能不能设计出别的辅助体?关键是按祖晅定理的条件构成图形。下面我们来介绍两个新的比课本上更简单的辅助体。设计一:如图1,乙为一躺放着的四棱锥P-ABCD,底ABCD为矩形,BC=2π~(1/2)R,CD=R,PD底ABCD,PD=π~(1/2)R. When using the ancestral hall principle to calculate the volume of the ball, an auxiliary body must be designed. In the textbook “Solid Geometry,” a circular cylinder whose base radius is equal to height is designed, and an inverted cone is removed in the middle. In addition to this auxiliary body, can not design other auxiliary bodies? The key is to form the graph according to the conditions of the ancestral hall. Below we introduce two new simpler aids than textbooks. Design one: As shown in figure 1, B is a quadrangular pyramid P-ABCD lying on the bottom, bottom ABCD is rectangular, BC=2π~(1/2)R, CD=R, PD bottom ABCD, PD=π~(1 /2) R.