解题方法
1 . 在正三棱锥
中,侧棱
,底面边长
,设点
在平面
上的正投影为
.连接
并延长交
于点
.
![](https://img.xkw.com/dksih/QBM/2020/9/1/2540573234184192/2543474605858816/STEM/78f2d359-4f6d-4e3b-a0a4-8d00966fb4a0.png?resizew=213)
(1)求证:
为
的中点;
(2)若过点
且平行于底面
的平面与
、
、
分别交于点
、
、
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c9afe5837b9e42137d69bb1658ae43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c157ff302a881c17514534903c575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2020/9/1/2540573234184192/2543474605858816/STEM/78f2d359-4f6d-4e3b-a0a4-8d00966fb4a0.png?resizew=213)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e527171b2a771265e3d56b64edf16054.png)
您最近一年使用:0次
名校
解题方法
2 . 已知梯形
中,
,
,
,
,
分别是
,
上的点,
,
,沿
将梯形
翻折,使平面
平面
(如图).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/0966c234-3aa3-4983-99d6-65cfbaf4312e.png?resizew=309)
(1)当
时,①证明:
平面
;②求二面角
的余弦值;
(2)三棱锥
的体积是否可能等于几何体
体积的
?并说明理由.
![](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/a8d3947804a878a87052c266be475423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fcb0ab3b6099434e4cdde2ea871f3f1.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d459cad63e3cd2aba10862800fa4832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c30f73c718bde8352055a14987fc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d8c77f758b4a06c320be39ecb328f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e826b8202fa0e17245dcc68426c923a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/0966c234-3aa3-4983-99d6-65cfbaf4312e.png?resizew=309)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febe72169c8dd4ecb57eadf7256dcbeb.png)
(2)三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67445ee86986aa474e8d71641d46b2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b575beb309541b02c629700b21e9c8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d86ab7c97cd8a0b15ba5efc1be94230.png)
您最近一年使用:0次
2020-08-16更新
|
1425次组卷
|
7卷引用:浙江省绍兴市鲁迅中学2019-2020学年高二上学期期中数学试题
解题方法
3 . 如图,平面
平面
,四边形
和
都是边长为2的正方形,点
,
分别是
,
的中点,二面角
的大小为60°.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/5544b738-f251-4406-a591-39165fd33071.png?resizew=190)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ec097d894a854d83946648f8b5fee9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05b05f4f031889c7f5c0e1750804c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03edbab2be470153ed4ebe16c25430b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/5544b738-f251-4406-a591-39165fd33071.png?resizew=190)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab71ff19bd011f08cc4d379dde1b6eab.png)
您最近一年使用:0次
2020-03-21更新
|
517次组卷
|
3卷引用:2020届湖北省随州市高三下学期3月调研考试数学(文)试题
4 . 如图所示,在四边形
中,
,
,
.将四边形
沿对角线
折成四面体
,使平面
平面
,则下列结论中正确的结论个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/0ceae6b6-f6b1-4138-a992-bca96069709f.png?resizew=237)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/408f7d9f-5fc9-44d1-b4cb-9050bc89ccd7.png?resizew=233)
①
;②
;
③
与平面
所成的角为
;
④四面体
的体积为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832afec35b94e7f73af80164b2b81c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bdfb0e1be5583e794ab614a8abe1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9c7cbcc38b28d45c8539710e5b260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe052786101dfcc941480919eb2cecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/0ceae6b6-f6b1-4138-a992-bca96069709f.png?resizew=237)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/408f7d9f-5fc9-44d1-b4cb-9050bc89ccd7.png?resizew=233)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b219a74a1ce5a2b22c36d8de1e21ff91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910fab9c432cda7e4642535638046094.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a037b1a3ec2e37bbcb05d0a467efb511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd148d264bc9043396f777523e907aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
④四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-03-05更新
|
602次组卷
|
6卷引用:湖北省随州市2018-2019学年高一下学期期末数学试题
湖北省随州市2018-2019学年高一下学期期末数学试题湖北省孝感市2018-2019学年高一下学期期末数学试题(已下线)【新东方】新东方高二数学试卷302(已下线)狂刷39 立体几何的综合-学易试题君之小题狂刷2020年高考数学(理)湖北省襄阳市2018-2019学年高一下学期期末数学试题(已下线)【新东方】杭州新东方高中数学试卷332
名校
5 . 三棱柱的底面是正三角形,侧棱垂直于底面,它的侧面展开图是边长分别为6和4的矩形,则它的体积为
A.![]() | B.![]() | C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2020-02-19更新
|
412次组卷
|
5卷引用:湖北省随州市2018-2019学年高一下学期期末数学试题
湖北省随州市2018-2019学年高一下学期期末数学试题湖北省襄阳市2018-2019学年高一下学期期末数学试题黑龙江省哈尔滨市德强高中2019-2020学年高一下学期数学期末试题(已下线)8.1 基本立体图形(第1课时)棱柱、棱锥、棱台(分层作业)-【上好课】(已下线)8.3简单几何体的表面积与体积——课堂例题
6 . 如图,已知
是正三角形,EA,CD都垂直于平面ABC,且
,
,F是BE的中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/1cd2b33c-38ca-454a-aaad-06129f6e735a.png?resizew=149)
求证:(1)
平面ABC;
(2)
平面EDB.
(3)求几何体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f36701e643b5ae1718aa5ce1f311601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/1cd2b33c-38ca-454a-aaad-06129f6e735a.png?resizew=149)
求证:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef11392fadd7dbccb073e416279993b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a22d6b860f06fe23618b0d3de6768fa.png)
(3)求几何体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7eee5e1864159d8242a206147b0c89.png)
您最近一年使用:0次
2019-08-01更新
|
1556次组卷
|
5卷引用:湖北省随州市2018-2019学年高一下学期期末数学试题
名校
7 . 如图所示的圆锥的体积为
,圆
的直径
,点C是
的中点,点D是母线PA的中点.
(1)求该圆锥的侧面积;
(2)求异面直线PB与CD所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5d2f9b48d6089c071cca7967792c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
(1)求该圆锥的侧面积;
(2)求异面直线PB与CD所成角的大小.
![](https://img.xkw.com/dksih/QBM/2018/9/7/2027160392228864/2043428171808768/STEM/96a3a1a1f120433aab84f6fa82937860.png?resizew=169)
您最近一年使用:0次
2018-09-30更新
|
367次组卷
|
2卷引用:湖北省随州市第二高级中学2018-2019学年高二9月起点考试(B+C班)数学试题
名校
8 . 如图,正方体
的棱长为2,动点E,F在棱上
.点G是AB的中点,动点P在
棱上,若
,则三棱锥
的体积
![](https://img.xkw.com/dksih/QBM/2018/9/7/2027160392228864/null/STEM/d3db040e61b4497db96ee833aafb11c2.png?resizew=116)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a99be053c95aefbebe7460e50df572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ec9b4b66ef4ae6649602b1bd06e422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e416ca9e681b92c492cfedfa19b05e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fc71669a773477567df321a90853be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb893928b17edb4efda73722fb66e36f.png)
![](https://img.xkw.com/dksih/QBM/2018/9/7/2027160392228864/null/STEM/d3db040e61b4497db96ee833aafb11c2.png?resizew=116)
A.与![]() | B.与![]() |
C.与![]() ![]() | D.与![]() ![]() |
您最近一年使用:0次
2018-09-30更新
|
258次组卷
|
2卷引用:湖北省随州市第二高级中学2018-2019学年高二9月起点考试(B+C班)数学试题
9 . 如图所示,在四棱锥
中,
平面
,
,
是
的中点,
是
上的点,
为△
中
边上的高.
(1)证明:
平面
;
(2)若
,
,
,求三棱锥
的体积;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17622ea6f6f5afd1ad817a557e5889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d773180e830c8a01294827ff81091b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7ee687c3ad4a6e97315491c619fc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199098479c92e87304b91871172d46e0.png)
![](https://img.xkw.com/dksih/QBM/2017/11/26/1825587474358272/1826876616990720/STEM/bcd4885de0ce4769b6fe79388fb54071.png?resizew=324)
您最近一年使用:0次
2017-11-28更新
|
659次组卷
|
3卷引用:湖北省随州市第二高级中学2018-2019学年高二9月起点考试(B+C班)数学试题
10 . 如图所示,四棱锥P-ABCD,底面ABCD是边长为2的正方形,PA⊥面ABCD,PA=2,过点A作AE⊥PB,AF⊥PC,连接EF.
(1)求证:PC⊥面AEF.
(2)若面AEF交侧棱PD于点G(图中未标出点G),求多面体P—AEFG的体积.
(1)求证:PC⊥面AEF.
(2)若面AEF交侧棱PD于点G(图中未标出点G),求多面体P—AEFG的体积.
![](https://img.xkw.com/dksih/QBM/2011/8/30/1570296013905920/1570296019312640/STEM/bc92472a09ae46baa4306d453e959556.png?resizew=279)
您最近一年使用:0次