解题方法
1 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
平面
,
,设点M为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/93a9146d-8dea-49b8-99d7-c8d2124b3ecc.jpg?resizew=189)
(1)若四棱锥
的体积为2,求异面直线
,
所成角的余弦值;
(2)若二面角
的余弦值为
,求
的长.
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d11dd7422f4703763abc23d83c7584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/93a9146d-8dea-49b8-99d7-c8d2124b3ecc.jpg?resizew=189)
(1)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c123937cd5c0769090771598d6aee7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08e91d2fa9519a5f48d488176700499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2021-01-28更新
|
94次组卷
|
2卷引用:河南省三门峡市2020-2021学年高二上学期期末数学(理科)试题
2 . 甲、乙两人进行比赛,现有两组图形,第一组为一个正方形及其外接圆和内切圆,第二组为一个正方体及其外接球和内切球,甲在第一组图形内部任取一点,则此点在正方形与其外接圆之间得3分,此点在内切圆与正方形之间得2分,此点在内切圆内部得1分,乙在第二组图形内部任取一点,则此点在正方体与其外接球之间得3分,此点在内切球与正方体之间得2分,此点在内切球内部得1分.
(1)分别求出甲得3分的概率和乙得3分的概率;
(2)预估在这种规则下,甲、乙两人谁的得分多.
(1)分别求出甲得3分的概率和乙得3分的概率;
(2)预估在这种规则下,甲、乙两人谁的得分多.
您最近一年使用:0次
解题方法
3 . 如图,三棱柱
中,侧面
是边长为2的菱形,
平面
,且
,点
为
的中点,
为
与
的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/a90a269a-c463-4131-8e8f-b7b492330b15.png?resizew=149)
(1)证明:
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/a90a269a-c463-4131-8e8f-b7b492330b15.png?resizew=149)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50eda31bbc3d40f0b305d4ac673fc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9f99fb3252a4b3b7a62e8a675ddce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682f59fc4d85044aae6082314438eb62.png)
您最近一年使用:0次
2020-12-13更新
|
146次组卷
|
2卷引用:河南省名校联盟2020-2021学年高二上学期期中考试 数学(理科)试题
名校
解题方法
4 . 如图所示,三棱柱
中,
底面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba724ccdc619779cf621504c6f48f35.png)
![](https://img.xkw.com/dksih/QBM/2020/11/30/2604337002094592/2604733353820160/STEM/9902d69b-ab2e-44b0-ae22-3790e2db8288.png?resizew=206)
(1)求证:
平面
;
(2)已知
且异面直线
与
所成的角为
,求三棱柱
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba724ccdc619779cf621504c6f48f35.png)
![](https://img.xkw.com/dksih/QBM/2020/11/30/2604337002094592/2604733353820160/STEM/9902d69b-ab2e-44b0-ae22-3790e2db8288.png?resizew=206)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4af4263fd109b4817deb6583b790f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
您最近一年使用:0次
2020-12-01更新
|
779次组卷
|
3卷引用:河南省温县第一高级中学2021-2022学年高二下学期开学考试文科数学试题
名校
解题方法
5 . 某几何体的三视图如下,其中俯视图的内外均为正方形,边长分别为
和
,几何体的高为
,求此几何体的表面积和体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://img.xkw.com/dksih/QBM/2020/11/9/2589447185227776/2591149047971840/STEM/d37de08c73834cf797891acf96467efe.png?resizew=256)
您最近一年使用:0次
2020-11-12更新
|
459次组卷
|
3卷引用:河南省焦作市县级重点中学2021-2022学年高二上学期期中数学(文科)试题
名校
解题方法
6 . 如图,在四棱锥
中,底面
是平行四边形,
,侧面
底面
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261204631552/2542443310964736/STEM/06305e9c-8810-4ede-9ec2-5ba57a5f9a33.png?resizew=153)
(1)求证:
平面
;
(2)过
的平面交
于点
,若
,求三棱锥
的体积.
![](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/c5b0382c28547d3834ca71f3f0677695.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/e99998f33ad6edab18180627d4903dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaa14690732aac2d2b8e2561ebbc047.png)
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261204631552/2542443310964736/STEM/06305e9c-8810-4ede-9ec2-5ba57a5f9a33.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9f5de9503f4d71588c16b0ac33742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd3b6cf2e17d221c8aaeb70e81ef48.png)
您最近一年使用:0次
2020-09-04更新
|
385次组卷
|
3卷引用:河南省鹤壁市高级中学2020-2021学年高二上学期阶段性检测(二)数学试题
名校
解题方法
7 . 如图所示,在四棱锥
中,底面
为平行四边形,
,
,且
底面
.
![](https://img.xkw.com/dksih/QBM/2020/8/15/2528240295264256/2531127757742080/STEM/e6e3e8b491b44fecb1479bd3409be5fe.png?resizew=298)
(1)证明:
平面
;
(2)若
为
的中点,求三棱锥
的体积.
![](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/abc28e69c1ba0aac981256887f7dfa94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f15f3725dc69af03fb68c639796c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2020/8/15/2528240295264256/2531127757742080/STEM/e6e3e8b491b44fecb1479bd3409be5fe.png?resizew=298)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e40a351eff6e90e3008328eca0cc8f.png)
您最近一年使用:0次
2020-08-19更新
|
265次组卷
|
4卷引用:河南省信阳高级中学2021-2022学年高二下学期期末考试数学(文科)试题
河南省信阳高级中学2021-2022学年高二下学期期末考试数学(文科)试题河南省洛阳市第一高级中学2022届高三数学终极猜题卷全国卷(文)试题湖北省武汉市华中师范大学第一附属中学2020届高三下学期高考押题考试文科数学试题(已下线)专题20 立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅱ专版)
名校
解题方法
8 . 在三棱柱
中,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/004af439-71db-43f0-a0a7-f4f712726e65.png?resizew=200)
(1)证明:
//平面
;
(2)若
,点
在平面
的射影在
上,且侧面
的面积为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab02ac2021ead8554989d2612f118f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/004af439-71db-43f0-a0a7-f4f712726e65.png?resizew=200)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40154fd2f71e4621d800834f3656fd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8511a1b768df56495af12fc303f869dd.png)
您最近一年使用:0次
2020-08-18更新
|
885次组卷
|
12卷引用:河南省信阳高级中学2020-2021学年高二下学期回顾测试数学(文)试题
河南省信阳高级中学2020-2021学年高二下学期回顾测试数学(文)试题江西省南昌市三校2018-2019学年高二下学期期末数学(文)试题(一中、十中、铁一中)中原名校2019-2020学年高三下学期质量考评一数学文科试题中原名校2019-2020学年下学期质量考评一高三数学(文科)试题2017届山西省高三3月高考考前适应性测试(一模)数学(文)试卷吉林省吉林市2020届高三第四次调研测试数学(文)试题四川省泸州市泸县第二中学2020届高三下学期第二次高考适应性考试数学(文)试题(已下线)专题19 立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅲ专版)广西南宁市第二中学2021届高三上学期数学文科10月份考试试题(已下线)专题19 立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅰ专版)(已下线)易错点10 立体几何中的距离-备战2021年高考数学(文)一轮复习易错题山西省晋中市祁县中学2021届高三上学期12月月考数学(文)试题
名校
解题方法
9 . 如图,在四棱锥
中,
平面
,四边形
是矩形,
,
,
是
的中点,
,垂足为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/14851c84-bb74-414d-876a-4c80ec992c87.png?resizew=152)
(1)证明:
平面
.
(2)求三棱锥
的体积.
![](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/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f392902d611863c6908a48e696e7bd8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/14851c84-bb74-414d-876a-4c80ec992c87.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68744081315689b14c9c7a2b74100f46.png)
您最近一年使用:0次
2020-08-03更新
|
877次组卷
|
3卷引用:河南省新乡市新乡县第一中学2019-2020学年高二下学期期末考试数学(文)试题
解题方法
10 . 如图,在三棱柱ABC﹣A1B1C1中,侧面ABB1A1和侧面BCC1B1都是边长为2的菱形,且∠BAA1=∠CBB1=
.
![](https://img.xkw.com/dksih/QBM/2020/7/27/2515114414956544/2515491264831488/STEM/b3abc76668254084b7c519b3b90ae0d6.png?resizew=272)
(1)证明:BB1⊥A1C;
(2)若A1C=
.求三棱柱ABC﹣A1B1C1的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://img.xkw.com/dksih/QBM/2020/7/27/2515114414956544/2515491264831488/STEM/b3abc76668254084b7c519b3b90ae0d6.png?resizew=272)
(1)证明:BB1⊥A1C;
(2)若A1C=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
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2020-07-28更新
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319次组卷
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2卷引用:河南省平顶山市2019-2020学年高二(下)期末数学(文科)试题