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在新课标人教A版高中数学必修2~([1])中,我们认识了一些常见的空间几何体——柱体、锥体、台体、球体.其中台体是用一个平行于锥体底面的平面去截锥体,取底面与截面之间的部分得到的,其上、下底面关于原锥体的顶点位似,由锥体的体积公式不难推出台体的体积公式.若对台体的一个底面作适当形变,得到一个两底面不再相似的空间多面体,该如何去计算其体积呢?我们以一个简单的六面体ABCD-EFGH为
In the new curriculum standard to teach A version of high school mathematics compulsory 2 ~ ([1]), we know some common spatial geometry - cylinder, cone, table body, sphere, which is a body with a parallel to the cone Take the plane of the bottom of the body to get the truncated cone, take the part between the bottom surface and the cross section, the top and bottom surfaces are similar to the top of the original cone, and it is not difficult to introduce the volume formula of the body from the volume formula of the cone. How to calculate the volume of a volumetric polyhedron on the base of a base body by a suitable deformation of a bottom surface of the base body to get a two-dimensional polyhedron is no longer similar? We use a simple hexahedron ABCD-EFGH