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近年高考及其模拟试题中的空间轨迹问题对考查学生的空间想象能力及转化化归能力都有较好的作用.现举几例,供参考.例1如图1,在棱长为2的正方体ABCD-A1B1C1D1中,点M在AA1上,点N在平面ABCD内,MN=AB,则MN的中点P的轨迹与正方体表面围成的较小的几何体的体积是().
In recent years, the spatial trajectory problem in the college entrance examination and simulation test questions has a good effect on the examination of students’ spatial imagination ability and transformation ability. Here are a few examples for reference. Example 1 is shown in Figure 1, with an edge length of 2 In the cube ABCD-A1B1C1D1, the point M is on AA1, the point N is on the plane ABCD, MN=AB, and the trajectory of P at the midpoint of MN and the volume of the smaller geometry surrounded by the cube surface are ().