名校
1 . 如图所示,圆锥SO的底面圆半径
,母线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/7eb2a967-f90b-4d58-98c4-4910fdc0ac9a.png?resizew=149)
(1)求此圆锥的体积和侧面展开图扇形的面积;
(2)过点O在圆锥底面作OA的垂线交底面圆圆弧于点P,设线段SO中点为M,求异面直线AM与PS所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2057edff5cd4864dc53c3b52805ba117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e456265c35938ebef2fb65cda3dd69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/7eb2a967-f90b-4d58-98c4-4910fdc0ac9a.png?resizew=149)
(1)求此圆锥的体积和侧面展开图扇形的面积;
(2)过点O在圆锥底面作OA的垂线交底面圆圆弧于点P,设线段SO中点为M,求异面直线AM与PS所成角的大小.
您最近一年使用:0次
2022-10-19更新
|
328次组卷
|
3卷引用:上海市徐汇区2019-2020学年高三上学期第一次模拟数学试题
名校
解题方法
2 . 如图,AB是圆柱的底面直径,AB=2,PA是圆柱的母线且PA=2,点C是圆柱底面圆周上的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/ea1ef0aa-b54e-40c8-a6de-89b11f418c1f.png?resizew=177)
(1)求圆柱的侧面积和体积;
(2)若AC=1,D是PB的中点,点E在线段PA上,求CE+ED的最小值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/ea1ef0aa-b54e-40c8-a6de-89b11f418c1f.png?resizew=177)
(1)求圆柱的侧面积和体积;
(2)若AC=1,D是PB的中点,点E在线段PA上,求CE+ED的最小值.
您最近一年使用:0次
2022-10-17更新
|
553次组卷
|
6卷引用:上海市行知中学2018-2019学年高二下学期期中数学试题
解题方法
3 . 如图,矩形
所在平面垂直于直角
所在平面,
,
,
,点
在
上且
,
为
的中点,
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/e253f2a8-607b-4ad6-8e63-ca2eb38d44fe.png?resizew=138)
(1)证明:
平面
;
(2)若三棱锥
的体积为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c013bbe1fb6e9acf461548b5cf6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf23e73ae2a15c04bbed3981cb8e511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/e253f2a8-607b-4ad6-8e63-ca2eb38d44fe.png?resizew=138)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a20ea69475dcf57a5ff18c13eceaaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55a8898c347a62c7de2bdca3f3c7e33.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e84059306d1173e38fe3437cc13daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d74ef32584586ec4857acd0a3f4fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
4 . 如图,直三棱柱
中,
,D、E在线段
上,且
,过
作与
平行的平面交
于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/28/45ac1c52-f96b-4828-b669-1bec2bd8ee5c.png?resizew=196)
(1)证明:平面
平面
;
(2)若三棱锥
的体积为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1555f5f7ef03b93fefae837469bdb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae2ed4da8e39f2467a6f211832e720e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e516121599c9fcc528121c00afcf52fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/28/45ac1c52-f96b-4828-b669-1bec2bd8ee5c.png?resizew=196)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d02824dd2cb82382c4127f9be2d15ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218c24785ab63c93c79a7c9e9da6e287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c9298da3cd8b9db58692e0173f3fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
解题方法
5 . 如图,在四棱锥
中,
平面
,底面
是菱形,
,
是线段
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/bc671e65-20a7-43f6-a38f-53fa12e17eaf.png?resizew=165)
(1)若
是线段
中点时,证明:
平面
;
(2)若直线
与底面
所成角的正弦值为
,且三棱锥
的体积为
,请确定
点的位置,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8918f85b19108d7d8d44aa163ecb70.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/ca19a96feba82dac65495f592bd89f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/bc671e65-20a7-43f6-a38f-53fa12e17eaf.png?resizew=165)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ac267d6d31c0796de694cf73ab8019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e0e41161f1a27e26d6f0b25941d55d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c76e558109d9b8dd700c1a7f9cc73ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2022-09-21更新
|
860次组卷
|
5卷引用:湖北省鄂东南省级示范高中教育教学改革联盟校2017-2018学年高二下学期期中考试数学(文)试题
湖北省鄂东南省级示范高中教育教学改革联盟校2017-2018学年高二下学期期中考试数学(文)试题(已下线)第35讲 利用传统方法解决立体几何中的角度与距离问题-2022年新高考数学二轮专题突破精练(已下线)9.4 空间角与空间距离(已下线)专题15 立体几何(讲义)-2(已下线)8.5.2直线与平面平行(精练)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
名校
解题方法
6 . 如图,在三棱锥
中,
,M为PB的中点,D为AB的中点,且
为正三角形
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/fb131d8d-cc97-4633-97c3-254774ba84c9.png?resizew=167)
(1)求证:
平面PAC
(2)若
,三棱锥
的体积为1,求点B到平面DCM的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be272b16df732d93adc4d6cc5e266ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4b0c4b339f44bbac0e275eb0718234.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/fb131d8d-cc97-4633-97c3-254774ba84c9.png?resizew=167)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3a44d5001ed4f043d1cf1e1842ee42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2022-09-21更新
|
845次组卷
|
7卷引用:广东省化州市2018届高三上学期第二次高考模拟考试数学(文)试题
广东省化州市2018届高三上学期第二次高考模拟考试数学(文)试题【全国市级联考】新疆乌鲁木齐地区2018届高三5月适应性训练数学文试题(已下线)2017-2018学年度下学期高一数学期末备考总动员A卷贵州省遵义市绥阳中学2019届高三模拟卷(一)文科数学试题2019届福建省福州第一中学高三上学期开学质检数学(文)试题(已下线)9.4 空间角与空间距离广东省广州市番禺区实验中学2022-2023学年高二上学期期中数学试题
7 . 如图,四面体ABCD中,O、E分别是BD、BC的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba593745d89c16c9fcf60800f30fdc1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/20/3dda0917-20dc-451b-9260-768f12a9dbc9.png?resizew=253)
(1)求证:
平面BCD;
(2)求异面直线AB与CD所成角的大小;
(3)求点E到平面ACD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba593745d89c16c9fcf60800f30fdc1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/20/3dda0917-20dc-451b-9260-768f12a9dbc9.png?resizew=253)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
(2)求异面直线AB与CD所成角的大小;
(3)求点E到平面ACD的距离.
您最近一年使用:0次
2022-09-20更新
|
935次组卷
|
5卷引用:2006年普通高等学校招生考试数学(理)试题(福建卷)
解题方法
8 . 如图,在三棱锥
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/18/fbf80a4a-d105-4463-9d0d-172c28c80de5.png?resizew=149)
(1)证明:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61e0bc2c17b9c34930c4a6c54e9a60b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/18/fbf80a4a-d105-4463-9d0d-172c28c80de5.png?resizew=149)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
您最近一年使用:0次
名校
解题方法
9 . 如图所示,在三棱柱ABC-A1B1C1中,侧面ACC1A1为菱形,∠A1AC=60°,AC=2,侧面CBB1C1为正方形,平面ACC1A1⊥平面ABC.点M为A1C的中点,点N为AB的中点.
(1)证明:MN∥平面BCC1B1;
(2)求三棱锥A1-ABC1的体积.
(1)证明:MN∥平面BCC1B1;
(2)求三棱锥A1-ABC1的体积.
您最近一年使用:0次
2022-07-08更新
|
462次组卷
|
8卷引用:湖北省华大新高考联盟2020届高三下学期4月教学质量测评数学(文)试题
10 . 如图,在四棱锥P-ABCD中,PC⊥底面ABCD,ABCD是直角梯形,AD⊥DC,AB∥DC,AB=2AD=2CD=2,点E是PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/30dd76af-e956-4fb4-9ad1-1fc6c9d2643a.png?resizew=183)
(1)证明:平面EAC⊥平面PBC;
(2)若直线PB与平面PAC所成角的正弦值为
;
①求三棱锥P-ACE的体积;
②求二面角P-AC-E的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/30dd76af-e956-4fb4-9ad1-1fc6c9d2643a.png?resizew=183)
(1)证明:平面EAC⊥平面PBC;
(2)若直线PB与平面PAC所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
①求三棱锥P-ACE的体积;
②求二面角P-AC-E的余弦值.
您最近一年使用:0次
2022-07-05更新
|
2837次组卷
|
8卷引用:重庆市名校联盟2021届高三上学期第二次联合测试数学试题
重庆市名校联盟2021届高三上学期第二次联合测试数学试题江苏省宿迁市沭阳县修远中学2020-2021学年高三(艺术班)上学期第四次质量检测数学试题北京十一学校2020-2021学年高二上期末数学试题北京市十一学校2020-2021学年高二上学期期末考试数学试题(已下线)第02讲 基本图形的位置关系(3)(已下线)专题08 立体几何综合-备战2023年高考数学母题题源解密(新高考卷)空间向量的应用(已下线)7.5 空间向量求空间角(精练)