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把一个几何体纳入一个更大的几何体内的补形技巧,是化解几何体表面积与体积计算中难点的方法之一.本文就近几年的一些高考题和模拟题,剖析把不规则的多面体纳入规则的长方体内的补形技巧.设长方体共顶点的三条棱长分别为a,b,c,体对角线长为l,表面积为S,体积为V,外接球半径为R,则有l~2=a~2+b~2+c~2,S=2(ab+ac+bc),V=abc,l=2R.
One of the ways to solve a difficult problem in geometric calculation of surface area and volume is to take a geometric body into a larger geometric body.This paper analyzes some entrance exam questions and simulated questions in recent years and analyzes the irregular polyhedron into the rules The rectangular shape of the complementing skills set the total length of the cuboid total of three prism length a, b, c, the body diagonal length l, the surface area of S, the volume of V, the external ball radius R, then l ~ 2 = a ~ 2 + b ~ 2 + c ~ 2, S = 2 (ab + ac + bc), V = abc, l = 2R.