名校
解题方法
1 . 设
是两个不同的平面,m,l是两条不同的直线,则下列命题为真命题的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
2024-04-16更新
|
410次组卷
|
13卷引用:2024年九省联考试卷分析及真题鉴赏
2024年九省联考试卷分析及真题鉴赏2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题1-5专题10空间中点线面的位置关系(已下线)专题8.11 立体几何初步全章十四大压轴题型归纳(拔尖篇)-举一反三系列(已下线)第八章立体几何初步(单元测试)-【上好课】-(人教A版2019必修第二册)(已下线)核心考点5 立体几何中的位置关系 A基础卷 (高一期末考试必考的10大核心考点)山东省济南市2023-2024学年高二上学期期末质量检测模拟数学试题山东省青岛市第五十八中学2022-2023学年高一下学期5月阶段性模块考试数学试题山西省临汾市2024届高三第二次高考考前适应性训练数学试题单元测试B卷——第八章?立体几何初步福建省厦门双十中学2023-2024学年高二下学期开学考试数学试题新疆乌鲁木齐市第二十三中学2023-2024学年高一下学期5月月考数学试题
2 . 已知轴截面为正三角形的圆锥
的高与球
的直径相等,则圆锥
的体积与球
的体积的比值是__________ ,圆锥
的表面积与球
的表面积的比值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583f9d5300e46ca713b61d742df9c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583f9d5300e46ca713b61d742df9c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583f9d5300e46ca713b61d742df9c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2024-01-19更新
|
6008次组卷
|
6卷引用:2024年九省联考试卷分析及真题鉴赏
2024年九省联考试卷分析及真题鉴赏2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题11-15(已下线)专题05 空间向量与立体几何(分层练)(四大题型+21道精选真题)山东省济南市2023-2024学年高二上学期期末质量检测模拟数学试题福建省厦门双十中学2023-2024学年高二下学期开学考试数学试题
3 . 将边长为2的等边
沿
边中线
折起得到三棱锥
,当所得三棱锥体积最大时,点
到平面
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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4 . 如图,在四棱锥
中,平面
平面
,四边形
为正方形,
为等边三角形,点
在
上,
,点
为线段
的中点,点O为三角形
的重心.
(1)求证:
平面
;
(2)若四棱锥
的体积为
,求四棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b86b8bf99386fc939c9c12b1355ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905f4cbe939c528692f367fe34333216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b265d121f9ebc13671a5719604476a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/cb3d1c8d-94a1-45da-8d4c-33ebc434c20e.png?resizew=115)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc36cda92e01d6f85e9e2e6c0917ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2278dbf1ada5dc5289063e5f77c22b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
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解题方法
5 . 已知过点
的直线被圆
截得的弦为AB,若
为等边三角形,则直线AB的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab276155617fe201dcc71b5f1b54ab75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 如图是一个几何体的三视图,则该几何体的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/0a46e360-9caa-4acf-b7ce-c1c4c20b1d9b.png?resizew=122)
A.![]() | B.![]() | C.4 | D.8 |
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7 . 如图所示,在四棱锥
中,
底面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/3213df0b-c6b4-4afd-9f3f-99f55f4fcc80.png?resizew=151)
(1)求证:
;
(2)若
,求平面
和平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.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/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d40978fbe52316daaaa6bdbb403fea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/3213df0b-c6b4-4afd-9f3f-99f55f4fcc80.png?resizew=151)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2751630b7353ff6bce1e8e06a2a424e6.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
8 . 将四棱锥
沿棱展开为平面图形,如图所示.若
,
,
,
,
,
,则在展开图中,
两点之间的距离![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9214112843303e45a4d9dc20507ed1.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e07a099bf87e471b94bc97f0249daf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074a5b4d376ae0d7648d97b79be0b65d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d829c51c819076d094facd9dffe2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b7efcc776e3479d01484cd468c6894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa5088fedf996af3d7c50a39bdaae73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be94b5ac27724cd0e43541759203784e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0698ef3a8f862a82245d97691eba628f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9214112843303e45a4d9dc20507ed1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c6cb2c6f-7ab3-445d-8449-1c3850cd7f7f.png?resizew=171)
您最近一年使用:0次
解题方法
9 . 如图,在三棱柱
中,底面是边长为
的正三角形,已知平面
平面
,点
分别为棱
,
的中点,且
.
(1)求证:
平面
;
(2)若直线
与底面
所成角为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0c892fa3699be6f3b91013c644e773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea077cdc5c3aee9e46bf679477cb201.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/9d1b89a4-9d2d-408f-93d3-9000d66fb48a.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42605242ae45b6223b23b7a70a2b1618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61dc0fec2de4694075281e882d3c5ac.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6e972f1c678da0a16e8b532321ce4.png)
您最近一年使用:0次
10 . 已知三棱锥
中,
,则
,
,
与平面
所成角的正弦值的平方和( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4abd106436cb0e0281d66171aa7b5b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.与![]() ![]() ![]() |
B.为定值1 |
C.为定值![]() |
D.为定值2 |
您最近一年使用:0次