1 . 已知三棱锥
的四个顶点均在同一球面上,
,
,且三棱锥
体积的最大值为
,则该球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e45b0e1c3f6f5bc4cc81290bf263d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 如图所示,圆柱
的底面半径为
,
,
为圆
的直径,点
为圆
上的动点,点
为圆柱侧面上的动点(不含边界),
平面
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbf49977b753e293bdf415fccd91abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e245440d3761fb4217eaa8dc303fa288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4582305e012d3b7c3d73195af889de5.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
3 . 如图,平行四边形
中,
,
.现将
沿
起,使二面角
大小为120°,则折起后得到的三棱锥
外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cc201327a8ee3fd646948d3f0c5d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d35d8d8bb0dc17f2f86fe5b230a2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282d4a8c3476b2b81e3fd73898e64539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3931333820859378ea6723ff3075189.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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昨日更新
|
680次组卷
|
4卷引用:浙江省重点中学四校2023-2024学年高一下学期5月联考数学试题
4 . 正方体
中,
,
分别在
上,且
,
,则下列正确的有( )个
①
,②
,③
,④点
到平面
距离为1
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564a9f661332d97d09e82dfd6f499d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0963c102bfc6da34a4e8c4e16d503065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac240e81e4dbf3097c843b75235ec661.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e89457e4eafe86d2c6f404f967c753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661df691bacf67f20557fef29c1af1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6469878a955cc09fac22ba5aea3fb962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028856d5101687dd8eaf130846489cfd.png)
A.1 | B.2 | C.3 | D.4 |
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解题方法
5 . 如图,已知正方体
的棱长为1,点
为棱
的中点,点
在正方形
内部(不含边界)运动,给出以下三个结论:
①存在点
满足
;
②存在点
满足
与平面
所成角的大小为
;
③存在点
满足
;
其中正确的个数是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
①存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba0a98a9ba64282ec2e728b5c8bf2e6.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79039b211d151710a15fc9dda11d6225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc6128dc4ac8976672e033f336d947b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
③存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035da178acd379d26e906bc58994af83.png)
其中正确的个数是( ).
A.0 | B.1 | C.2 | D.3 |
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6 . 如图,在六面体
中,平面
平面
,四边形ABCD与四边形
是两个全等的矩形,
,
,
平面ABCD,
,
,
,则六面体
的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04de6e3d84ddf7da3dc4fab26e59df46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590dd3b109776fa5521dfc9eecdfb87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00194912b2521c3fe54d3b0af7563e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44c59421cc4ae05d95fec5ac13a761c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ef1ff132a7d10e2ab527571e61612c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d0fdc5a00ca0e857b89a7e1420df29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.288 | B.376 | C.448 | D.600 |
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解题方法
7 . 在长方体
中,已知
,
,
,点
为底面
内一点,若
和底面
所成角与二面角
的大小相等,点
在底面
的投影为点
,则三棱锥
体积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b59ab6bf6111dda4a3d428454768b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad3a1ea6790177130e16c2124984087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adebae2f9d7543915eb5a36427f9b6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e07010ccdf2d83b7d3a6944034d3c95.png)
A.![]() | B.2 | C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
8 . 已知正方体
和点
,有两个命题:
命题甲:存在
条过点
的直线
,满足
与正方体的每条棱所成角都相等;
命题乙:存在
个过点
的平面
,满足
与正方体的每个面所成锐二面角都相等;
则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
命题甲:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
命题乙:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
则下列判断正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
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9 . 如图,在棱长为2的正方体
中,E,F,G分别是
,
,
的中点,点P在线段
上,
平面
,则以下错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f05389f5270a557638d69fc0b0f9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f475878dd1b32b0486cbf7b5ffbedd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
A.![]() ![]() ![]() | B.点P为线段![]() |
C.三棱锥![]() ![]() | D.平面![]() ![]() |
您最近一年使用:0次
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解题方法
10 . 如图所示,已知正方体
的棱长为
分别是
的中点,
是线段
上的动点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18755b4aaf64e1d055018c8510f8f2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69ed30e30ec2020f0778986a40902ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.当点![]() ![]() ![]() |
B.平面![]() |
C.![]() |
D.![]() ![]() |
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