2024·全国·模拟预测
名校
1 . 已知平面
平面
,且均与球
相交,得截面圆
与截面圆
为线段
的中点,且
,线段
与
分别为圆
与圆
的直径,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414844edd458857bdfc80bffa61cbf9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32987e12782f888f4a6db40c5c3d13ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2892d380f9370caecf6ac7370b3a0737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
2 . 已知
,
,
,
为球面上四点,
,
分别是
,
的中点,以
为直径的球称为
,
的“伴随球”,若三棱锥
的四个顶点在表面积为
的球面上,它的两条边
,
的长度分别为
和
,则
,
的伴随球的体积的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc2a78406f5e1e9936c60851f6e9500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 在四棱锥
中,
是正方形,
,
,
,
为棱
上一点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc904a45c77013665ccfbb58f72135d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb64061e933aea7669294640c331bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add48f067e2ad2ab0a494c2eb071e3fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
A.点![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.四棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
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名校
解题方法
4 . “阿基米德多面体”也称为半正多面体(semi-regularsolid),是由边数不全相同的正多边形为面围成的多面体,它体现了数学的对称美.如图所示,将正方体沿交于一顶点的三条棱的中点截去一个三棱锥,共可截去八个三棱锥,得到八个面为正三角形、六个面为正方形的一种半正多面体.已知
,则关于如图半正多面体的下列说法中,正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
A.该半正多面体的体积为![]() |
B.该半正多面体的顶点数![]() ![]() ![]() ![]() |
C.该半正多面体过![]() ![]() |
D.该半正多面体外接球的表面积为![]() |
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2024-04-26更新
|
430次组卷
|
3卷引用:云南省昆明市云南师范大学附属中学2023-2024学年高一下学期教学测评期中卷数学试卷
2024·全国·模拟预测
名校
解题方法
5 . 已知圆锥
的轴截面是顶角为
的等腰三角形,其母线长为
,底面圆周上有
,
两点,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.截面![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若一只小蚂蚁从圆锥底面圆周上一点绕侧面一周回到原点,则最短路程为![]() |
D.当三棱锥![]() ![]() |
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6 . 如图,在棱长为2的正方体
中,点
分别为
的中点,
为面
的中心,则以下命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7beb3b41f243ab66df61975d712428fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.平面![]() ![]() |
B.四面体![]() ![]() |
C.四面体![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
7 . 在四棱锥
中,底面四边形
为等腰梯形,
,
,
是边长为2的正三角形,
,则四棱锥
外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d4e574c9d139615d991a168cfbf63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0026fed6a58ec0a5dbefbe03e5956162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
8 . 如图,在直三棱柱
中,
,
,
,侧面
的对角线交点
,点
是侧棱
上的一个动点,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d46c17903078e0b38279353c5430d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
A.直三棱柱的侧面积是![]() |
B.直三棱柱的外接球表面积是![]() |
C.三棱锥![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2024-04-19更新
|
1073次组卷
|
3卷引用:浙江省杭州市西湖高级中学2023-2024学年高一下学期4月期中测试数学试题
浙江省杭州市西湖高级中学2023-2024学年高一下学期4月期中测试数学试题广西南宁市第三中学2023-2024学年高一下学期月考(三)数学试题(已下线)专题6 组合体中的外接与内切问题【练】(高一期末压轴专项)
名校
9 . 在四棱锥
中,已知
,
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5259440a312d9f700bf1494c1697db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbddb854a1a634484936c64ab4a9102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b468c0ccddafc04a29802cf242723bde.png)
A.四棱锥![]() ![]() |
B.![]() ![]() |
C.四棱锥![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
2024-04-19更新
|
361次组卷
|
2卷引用:山西省部分学校2023-2024学年高三年级阶段性测试(定位)数学试题
名校
10 . 将边长为4的正方形
沿对角线
折起,使点
不在平面
内,则下列命题是真命题的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.不论二面角![]() ![]() |
B.当二面角![]() ![]() ![]() |
C.当二面角![]() ![]() ![]() |
D.不论二面角![]() ![]() ![]() |
您最近一年使用:0次