名校
解题方法
1 . 如图,在三棱锥
中,
,
,
,点
在平面
内,且
,设异面直线
与
所成的角为
,则
的最大值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/72ef084d-344d-403e-a2d4-13ee8d06ed94.png?resizew=190)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b83fa9f7991f178fc7efc4a940fc17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cb41eff34c1ec4ba2ea4f4f8700245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/72ef084d-344d-403e-a2d4-13ee8d06ed94.png?resizew=190)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-09-10更新
|
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12卷引用:北京市北京一零一中学2021-2022学年高二上学期期中考试数学试题
北京市北京一零一中学2021-2022学年高二上学期期中考试数学试题(已下线)期中模拟题(二)-2021-2022学年高二数学同步单元AB卷 (人教A版2019选择性必修第一册+第二册,浙江专用)浙江省金华市曙光学校2020-2021学年高二下学期第一次阶段考试数学试题江西省宜春中学2021-2022学年高二上学期第一次月考数学(理)试题陕西省西安市铁一中学2021-2022学年高二上学期第一次月考理科数学试题(已下线)2022年1月浙江省普通高中学业水平考试数学仿真模拟试卷A江西省鹰潭市2021-2022学年高二上学期期末数学(理)试题(已下线)专题16 空间向量及其应用(练习)-2河南省洛阳市新安县第一高级中学2022-2023学年高二上学期9月月考数学试题江苏省徐州市第七中学2022-2023学年高二下学期5月学情调研数学试题(已下线)期末模拟预测卷02(已下线)专题03 空间向量的应用压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)
名校
2 . “阿基米德多面体”也称为半正多面体,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,将正方体沿交于一顶点的三条棱的中点截去一个三棱锥,共截去八个三棱锥,得到的半正多面体的表面积为
,则关于该半正多面体的下列说法中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/12401610-f2fa-4097-8f4f-19df0aab0dcf.png?resizew=177)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2c06207565e9fa6a288a788e4ab2fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/12401610-f2fa-4097-8f4f-19df0aab0dcf.png?resizew=177)
A.与AB所成的角是60°的棱共有8条 |
B.AB与平面BCD所成的角为30° |
C.二面角![]() ![]() |
D.经过A,B,C,D四个顶点的球面面积为![]() |
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5卷引用:广东省广州市二中2021-2022学年高二上学期期中数学试题
广东省广州市二中2021-2022学年高二上学期期中数学试题山西省运城市康杰中学2021-2022学年高二上学期入学测试数学试题广东省深圳市第三高级中学2022届高三上学期9月第一次月考数学试题上海交通大学附属中学2023届高三下学期期中数学试题(已下线)第九章 立体几何专练10—二面角小题2-2022届高三数学一轮复习
名校
3 . 如图,在直三棱柱
中,
.
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720203138711552/2802149849358336/STEM/a6ee52f2-9763-463b-ac1d-89b8ce070d3b.png?resizew=197)
(1)求证:
;
(2)若
与
的所成角的余弦值为
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b9f991c511425863426684814779eb.png)
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720203138711552/2802149849358336/STEM/a6ee52f2-9763-463b-ac1d-89b8ce070d3b.png?resizew=197)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de9b94a20b9d6ea37cfe135d790801.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
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名校
解题方法
4 . 如图,在三棱锥
中,
底面
于
于
.若
,则
面积的最大值________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0c8b1bab83af0e80734e9915cf9368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8da7ba1b78ff2e5a6279ec10610bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edb43edea125db888afae751f7d1a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2331c755ff3034217ea3d9f45b25f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/19afb68f-8555-486a-9280-f93198ab15b4.png?resizew=111)
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名校
5 . 如图,在正方体
中,
,
,
分别是
,
,
的中点,则下列说法错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/7a2dd3c4-3252-4ea8-a1a3-95d12ed0abe2.png?resizew=200)
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/7a2dd3c4-3252-4ea8-a1a3-95d12ed0abe2.png?resizew=200)
A.![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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4卷引用:黑龙江省哈尔滨市哈尔滨师范大学附属中学2020-2021学年高一下学期期中数学试题
6 . 如图,在四棱锥
中,
底面
,四边形
中,
,
.
平面
;
(2)设
,若直线
与平面
所成角大小为30°,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21929cd5ce9120fe3b7ac99730b617b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9f566f9ab9c6f9498d5c69e9e98bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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3卷引用:上海市西南位育中学2020-2021学年高二下学期期中数学试题
上海市西南位育中学2020-2021学年高二下学期期中数学试题湖北省襄阳市第五中学2021-2022学年高二上学期10月月考数学试题(已下线)广东省佛山市第一中学2024届高三上学期第二次调研数学试题变式题17-22
名校
解题方法
7 . 祖暅原理也称祖氏原理,是我国数学家祖暅提出的一个求积的著名命题:“幂势既同,则积不容异”,“幂”是截面积,“势”是几何体的高,意思是两个同高的立体,如在等高处截面积相等,则体积相等.由曲线
围成的图形绕
轴旋转一周所得旋转体的体积为
,满足
的点
组成的图形绕
轴旋转一周所得旋转体的体积为
,则
满足以下哪个关系式( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1eefbd6916569abb8948abf46f02b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1598d8d2f784d7d62d7e8bc4628d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70e5fe4b4b828f623e2e309affb37ac.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
8 . 已知正三棱柱
的各棱长都是4,点
是棱
的中点,动点
在侧棱
上,且不与点
重合,设二面角
的大小为
,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01cca53693e4bc901899f3360d21618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e7645a53-2a2c-4711-8df1-739ba08c79be.png?resizew=157)
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4卷引用:上海市西南位育中学2020-2021学年高二下学期期中数学试题
上海市西南位育中学2020-2021学年高二下学期期中数学试题四川省乐山市十校2021-2022学年高二上学期期中考试数学(理)试题江西省赣州市赣县第三中学2021-2022学年高二9月考试数学(理)试题(已下线)第08讲 二面角(核心考点讲与练)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修第三册)
名校
解题方法
9 . 已知三棱锥
中,
两两垂直,且长度相等,若
都在半径为1的同一球面上,则球心到平面
的距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c7267e5313b9b00ef22c94a479fc34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531a88ee858d578a424650a2d42650bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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3卷引用:上海市西南位育中学2020-2021学年高二下学期期中数学试题
上海市西南位育中学2020-2021学年高二下学期期中数学试题(已下线)重难点02 几何体的表面积、体积、轴截面、多面体与球体内切外接问题 (重难点突破解题技巧与方法)-2022-2023学年高二数学考试满分全攻略上海市控江中学2022-2023学年高二下学期3月月考数学试题
名校
解题方法
10 . 在直三棱柱
中,
,点
是直线
上一动点,则
的最小值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b612ce36785ab1691d60a0d49fab18a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138e0045398b0f40258ae51abe8b6f72.png)
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