解题方法
1 . 已知一个球的表面上有四点
、
、
、
,
,
,
,平面
平面
,则该球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1719410d21e3de1242366ce2965e838c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef35540101a8d7331dfe62fd1ab4d674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
您最近一年使用:0次
2023-04-26更新
|
621次组卷
|
4卷引用:广西桂林市临桂区第三中学2024届高三下学期4月月考数学试卷
广西桂林市临桂区第三中学2024届高三下学期4月月考数学试卷河南省名校青桐鸣2023届高三下学期4月联考理科数学试题河南省名校青桐鸣2023届高三下学期4月联考文科数学试题(已下线)四川省巴中市2023届高三“一诊”考试数学(理)试题变式题11-15
名校
2 . 如图,在平面四边形
中,
,现将
沿
折起,并连接
,使得平面
平面
,若所得三棱锥
的外接球的表面积为
,则三棱锥
的体积为( )
![](https://img.xkw.com/dksih/QBM/2022/9/6/3060423308353536/3066133271535616/STEM/7ea9ef789c1d4d038851c7d36f9a7b7b.png?resizew=323)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9ca96b0480a345bc5a035ca539023d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9609625b502348556ff8ba32deac8caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://img.xkw.com/dksih/QBM/2022/9/6/3060423308353536/3066133271535616/STEM/7ea9ef789c1d4d038851c7d36f9a7b7b.png?resizew=323)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-09-14更新
|
2175次组卷
|
6卷引用:广西2023届高三上学期西部联考数学(理)试题
名校
解题方法
3 . 如图,在四棱锥P-ABCD中,底面ABCD为菱形,△PAD为正三角形,平面PAD⊥平面ABCD,E,F分别是AD,CD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/d11f74ff-c676-4480-b7bb-e7022989297a.png?resizew=224)
(1)证明:BD⊥PF;
(2)若AD=DB=2,求点C到平面PBD的距离;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/d11f74ff-c676-4480-b7bb-e7022989297a.png?resizew=224)
(1)证明:BD⊥PF;
(2)若AD=DB=2,求点C到平面PBD的距离;
您最近一年使用:0次
2021-11-29更新
|
1487次组卷
|
3卷引用:广西南宁市东盟中学2021届高三5月考数学(文)试题
广西南宁市东盟中学2021届高三5月考数学(文)试题宁夏石嘴山市第三中学2022届高三上学期第二次月考数学(文)试题(已下线)专题20 立体几何综合大题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
4 . 如图,在四棱锥
中,底面
为矩形,平面
平面
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/477cdcac-47cb-4566-a79d-191d74b1b6c3.png?resizew=193)
(1)求证:
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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25d999f95db52faddb9f0eb7306b4d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd751d6402876e3c41c0b689388709e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/477cdcac-47cb-4566-a79d-191d74b1b6c3.png?resizew=193)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
您最近一年使用:0次
2021-06-08更新
|
1146次组卷
|
3卷引用:广西南宁市第三中学2021届高三收网考数学(文)试题
广西南宁市第三中学2021届高三收网考数学(文)试题(已下线)7.3 空间几何体积及表面积(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)河北省武安市第一中学2022届高三上学期第四次调研数学试题
名校
解题方法
5 . 在正方体ABCDA1B1C1D1中,点P是线段BC1上任意一点,则下列结论中正确的是( )
A.AD1⊥DP | B.AP⊥B1C |
C.AC1⊥DP | D.A1P⊥B1C |
您最近一年使用:0次
2022-05-07更新
|
453次组卷
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4卷引用:广西壮族自治区桂林市田家炳中学2023届高三上学期11月月考数学(文)试题
广西壮族自治区桂林市田家炳中学2023届高三上学期11月月考数学(文)试题【全国百强校】重庆市第八中学2018届高考适应性月考(八)数学(文)试题(已下线)8.6.2空间直线、平面的垂直(2)(课后作业)【师说智慧课堂】新教材人教A(2019)必修(第二册)(已下线)专题08 立体几何中的平行与垂直问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)
6 . 如图,在四棱锥
中,四边形
是等腰梯形,
,
,
,三角形
是等边三角形,平面
平面
,
、
分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/1c433b7f-2c7d-4d1b-b037-4708e859c6db.png?resizew=195)
(1)求证:平面
平面
;
(2)若
,
,求
的值.
![](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/c15416b74b2ecbcfa38cf34a9ffff730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae139b51956b9281d73d9ba82b875e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448cbac9a1ef3de7538a6b30cdc39582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/1c433b7f-2c7d-4d1b-b037-4708e859c6db.png?resizew=195)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d1553f6806c1eee3b17b94d23f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b156bc439fbaba3bfc9937beccb9b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ce281401b92d11871867cf5a5fe199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0421a60cf7269fd9869c77c59a84d2a1.png)
您最近一年使用:0次
7 . 如图,
为矩形,且平面
平面
,
,
,
,
,点
是线段
上的一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/1ededf03-dad3-416b-a77b-c94b241c3f70.png?resizew=114)
(1)证明:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79a2017b602dfcba9f295c2a3157a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4746df85049d1651d3f6c30212a7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1c488ded1c1f4f68a88b104a097ef2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/1ededf03-dad3-416b-a77b-c94b241c3f70.png?resizew=114)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0180a58a753fced571fc00f0bee8ff0d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445b51117626fbd3373e32acc514c64b.png)
您最近一年使用:0次
2019-12-10更新
|
622次组卷
|
2卷引用:2020届广西壮族自治区钦州市第三中学高三下学期3月月考数学(理)试题
8 . 如图,在三棱柱
中,
是侧面
的对角线的交点,
分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/219cd2cc-61fb-4a2f-95b0-5a6ee73a4dd3.png?resizew=162)
(1)求证:
//平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede6a60cad0e0b58e1549fda6e085719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3699d142dbb9f8a1b3da278daf8ca034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c344152460611c87b1e04a487055861b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98842968c75427c940b34de391a3a778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977ab80da22c4ab5867877d325513dbc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/219cd2cc-61fb-4a2f-95b0-5a6ee73a4dd3.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f69f26d0ddf27ab715880f818df750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82e2c8444fdc3753a283e187f8d1e80.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da1f322721ac19a78658af66eff5669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16dd27701a0a9849b58d39ae10623763.png)
您最近一年使用:0次
9 . 如图,菱形
的对角线
与
相交于点
,
平面
,四边形
为平行四边形.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/96526fa1-4da4-429a-af15-931e084cdd25.png?resizew=176)
(1)求证:平面
平面
;
(2)若
,点
在线段
上,且
,三棱锥
的体积是四棱锥
体积的一半,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/befd9ccddb75aeb71cd1a008669f34da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db0b84c4bba1e131db2083d496cc48e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/96526fa1-4da4-429a-af15-931e084cdd25.png?resizew=176)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6dd051db98c531f9ef18cdfd793f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42252c944ceec6fa274fe54c8efbdf72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0610b3faee95f6a7ee79c6b4550dbcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314a608f5e040d4bfb18e757e5bc587d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5909679a1240886215514a7d644bafe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
10 . 如图,在四棱锥
中,
∥
,
,
,平面
平面
,
为等腰直角三角形,
.
![](https://img.xkw.com/dksih/QBM/2017/12/27/1847529561939968/1848757216231424/STEM/23f8042995c446ddbf4dd900053009fc.png?resizew=156)
(Ⅰ)证明:
;
(Ⅱ)若三棱锥
的体积为
,求
的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48bdf03637fef00421b29fa697102c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db8b0f0ac45b16388d408a60e69bcdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://img.xkw.com/dksih/QBM/2017/12/27/1847529561939968/1848757216231424/STEM/23f8042995c446ddbf4dd900053009fc.png?resizew=156)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9396a2523d078c7fafbdcf231a9e772d.png)
(Ⅱ)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b183492677d0457b8701c53d9fa1414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d7afb771b2ada6a98f6ae93baa76a8.png)
您最近一年使用:0次
2017-12-29更新
|
864次组卷
|
2卷引用:广西陆川县中学2018届高三12月月考数学(文)试题