名校
解题方法
1 . 已知直三棱柱
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/12/7/2867393608392704/2868877442506752/STEM/2dbb6858e68946e48247a7cc5cf2d1ec.png?resizew=132)
![](https://img.xkw.com/dksih/QBM/2021/12/7/2867393608392704/2868877442506752/STEM/7c2832dd27a5462f951b507436e5590f.png?resizew=223)
(1)若
为
的中点,证明:
平面
;
(2)将两块形状与该直三棱柱完全相同的木料按如图所示两种方案沿阴影面进行分割,把木料一分为二,留下体积较大的一块木料.根据你所学的知识,请判断采用哪一种方案会使留下的木料表面积较大,并求出这个较大的表面积和说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6baf49925a5bcb359b542d45067c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://img.xkw.com/dksih/QBM/2021/12/7/2867393608392704/2868877442506752/STEM/2dbb6858e68946e48247a7cc5cf2d1ec.png?resizew=132)
![](https://img.xkw.com/dksih/QBM/2021/12/7/2867393608392704/2868877442506752/STEM/7c2832dd27a5462f951b507436e5590f.png?resizew=223)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a4b438e2e6687c7cd55ea08bbaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb7e8ef610cb5588bd52755399921a.png)
(2)将两块形状与该直三棱柱完全相同的木料按如图所示两种方案沿阴影面进行分割,把木料一分为二,留下体积较大的一块木料.根据你所学的知识,请判断采用哪一种方案会使留下的木料表面积较大,并求出这个较大的表面积和说明理由.
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