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解题方法
1 . 如图,在矩形纸片
中,
,
,
是
上一点.现将纸片沿
,
进行折叠,使点
落在线段
上,记
,则
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/9bad6f74-81dc-4d81-8ccf-068d8a7a58b1.png?resizew=168)
(1)当
时,求三棱锥
的体积;
(2)若在线段
上存在一点
,使
,求
的取值范围;
(3)当
时,再将
沿
进行折叠,若点
正好落在线段
上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c965a6952c03e015132e8745d761b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb694cbeb731ec5638d81b3509b6631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1039e15ef55da7c7bb2dfd18f783f51f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/9bad6f74-81dc-4d81-8ccf-068d8a7a58b1.png?resizew=168)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
(2)若在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dafebaaf13781120dc57c277d0267c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b38a71ea8963e93f727ed2d42785ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffbb4e6b92463a41bd9460dac6b1ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
2 . 半正多面体是由两种或两种以上的正多边形围成的多面体.半正多面体体现了数学的对称美.如图在一个棱长为4的正方体中,
,
,……,
,过
三点可做一截面,类似地,可做8个形状完全相同的截面.关于截面之间的位于正方体正中间的这个几何体,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36fb8219ce5186e7bb59a132eb881ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ff01e2d34ecd3a793aefca53539ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05700c3d8a6eddac23d7ff80dcccccc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e2fff17f81d5d24e3c76039b7ed51b.png)
A.当此半正多面体是由正八边形与正三角形围成时,边长为2 |
B.当此半正多面体是由正方形与正三角形围成时,表面积是![]() |
C.当此几何体为半正多面体时![]() ![]() |
D.当此几何体是半正多面体时,可能由正方形与正六边形围成 |
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3 . 已知正方体
的棱长为
,
为
的中点,
为面
的中心,现将正方体绕直线
旋转一周,得一几何体
,则( )
![](https://img.xkw.com/dksih/QBM/2021/5/15/2721678119370752/2763256464621568/STEM/93a43912-9332-4003-a141-134b5e9329f9.png?resizew=260)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://img.xkw.com/dksih/QBM/2021/5/15/2721678119370752/2763256464621568/STEM/93a43912-9332-4003-a141-134b5e9329f9.png?resizew=260)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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4 . 如图,在三棱柱
中,底面为边长为
的正三角形,
在底面的射影为
中点且
到底面的距离为
,已知
分别是线段
与
上的动点,记线段
中点
的轨迹为
,则
等于(注:
表示
的测度,本题中
若分别为曲线、平面图形、空间几何体,分别对应为其长度、面积、体积)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/3f70fe68-408c-4eb9-b47e-fa834a0901b2.png?resizew=220)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cf3bff56a7f4ab6c0008e90823025d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9880952857950577055578875ab29141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0758f3ff9f1f7109024c1ef65536c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0758f3ff9f1f7109024c1ef65536c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef812f839622326a7d7027cc806aaeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa7d487586e3702f55cd2d6466654bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcca943ee165b1a3ff7e0cc5f463754b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1705916cfcc664e452ce95e2b99efdb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4202ea5932e486a5548914d0743c0b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe37c2a81276baca0f6987cb017e6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe37c2a81276baca0f6987cb017e6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4202ea5932e486a5548914d0743c0b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4202ea5932e486a5548914d0743c0b11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/3f70fe68-408c-4eb9-b47e-fa834a0901b2.png?resizew=220)
A.![]() | B.![]() | C.![]() | D.![]() |
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