名校
解题方法
1 . 泉州花灯技艺源于唐朝中期从形式上有人物灯、宫物灯、宫灯,绣房灯、走马灯、拉提灯、锡雕元宵灯等多种款式.在2024年元宵节,小明制做了一个半正多面体形状的花灯,他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,得到一个有十四个面的半正多面体,如图所示.已知该半正多面体的体积为
,M为
的中心,过M截该半正多面体的外接球的截面面积为S,则S的最大值与最小值之比( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d754c4ad51e4482e12a615d20a13fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.3 | D.9 |
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2 . 如图,已知斜三棱柱
的侧面
是菱形,
,
.
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c853c91c054b7e1cd0de891aeedc8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae571b7fbebf3f266bb955dac2c572e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3f9e8e58175cc46453515621e69193.png)
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名校
3 . 如图,在四棱锥
中,平面
平面
,
,底面
为等腰梯形,
,且
.
平面
;
(2)若点A到平面PBC的距离为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852847ba02c2b62abf27e9cc11f596a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若点A到平面PBC的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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解题方法
4 . 如图,在直三棱柱
中,
,
,
为
的中点.
平面
;
(2)若二面角
的余弦值为
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d331850e91390d587ccddcb892f977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
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7日内更新
|
1109次组卷
|
3卷引用:黑龙江省双鸭山市第一中学等校2024届高三第四次模拟数学试题
名校
解题方法
5 . 三棱锥
中,
是边长为
的正三角形,
, 若三棱锥的体积为
,则
长度的最小值为___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307d38cc7012c328f1f22aa793fe76d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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解题方法
6 . 某几何体的三视图如图所示,设三视图中三个直角顶点在该几何体中对应的点为P,则点P到它所对的面的距离为________ .
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7 . 已知点
,平面
经过原点
,且垂直于向量
,则点
到平面
的距离为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62e22179a6fc4ad5cf82ff12f9000d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6d1c93ed2f9754f4971d635cdf3c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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|
137次组卷
|
13卷引用:立体几何与空间向量-综合测试卷A卷
(已下线)立体几何与空间向量-综合测试卷A卷湖南省益阳市2022-2023学年高二上学期10月联考数学试题河南省豫北名校2022-2023学年高二上学期10月教学质量检测数学试题河南省郑州市第四高级中学2022-2023学年高二上学期期末数学试题安徽省马鞍山市第二中学2022-2023学年高二下学期开学考试数学试题江苏省扬州市宝应县2022-2023学年高二下学期期中数学试题湖湘名校教育联合体2023-2024学年高二上学期10月联考数学试题福建师范大学第二附属中学2023-2024学年高二上学期10月月考数学试题河南省信阳市商城县上石桥高级中学2023-2024学年高二上学期10月月考数学试题山西省朔州市怀仁市第一中学校2023-2024学年高二上学期第三次月考(11月)数学试题陕西省榆林市第一中学2023-2024学年高二上学期期中考试数学试题上海市复旦大学附属中学2023-2024学年高二年级6月教学质量调研数学试卷陕西省榆林市神木市第四中学2023-2024学年高二下学期开学检测考试数学试题
名校
8 . 如图所示,在三棱锥
中,
与AC不垂直,平面
平面
,
.
;
(2)若
,点M满足
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3e94fe16834409e7688a83fbf7d5ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1c142967ed69606a3287ded01fcf9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
您最近一年使用:0次
2024-06-11更新
|
876次组卷
|
3卷引用:河南省九师联盟2024届高三下学期5月联考数学试题
解题方法
9 . 如图,在三棱锥
中,
平面
,平面
平面
,
,
,
为线段
的中点.
;
(2)求三棱锥
的体积.
![](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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bae7599ad243c12d94325ad917f0a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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解题方法
10 . 如图,在四棱锥
中,
,
,
,
,E是棱
的中点,且
平面
,点F是棱
上的一点.
平面
;
(2)若直线
与平面
所成角的正弦值为
,求
的长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3127e871668524928e227680aadbe1a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5258a6f9c63914b9e2ec95b6d39313b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145709169e0b3f8a82776b37760512c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
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