1 . 如图所示的几何体中,四边形
是正方形,
平面
,
,E、F、G分别为
、
、
的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/86026b4e-0004-43d1-b941-478d2d6bd44f.png?resizew=205)
(1)证明:平面
平面
;
(2)求三棱锥
与四棱锥
的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f8a9f5bde69e88589152dc7efb9624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160ccfe256fc5347daa5e4cc26719512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a25db800df9e245c6a31d9d978eab5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/86026b4e-0004-43d1-b941-478d2d6bd44f.png?resizew=205)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14913cb4acc97deaa4a34418a2dd2feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9854839f8f7fe792cd83cf3aa8b093.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f834efc124ae567fa8a9fbd94aee5bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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解题方法
2 . 如图,在四棱锥
中,
,
,
,
平面
,E为PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/b473418a-2d80-4fb1-bb41-57257e6b4a1f.png?resizew=159)
(Ⅰ)证明:
平面
;
(Ⅱ)若
,求点E到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810227b082bd14dbcde85c3181841571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/b473418a-2d80-4fb1-bb41-57257e6b4a1f.png?resizew=159)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672757753ee4387ac9ce54467663a82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2021-08-12更新
|
1074次组卷
|
7卷引用:安徽省阜阳市太和第一中学2020-2021学年高三上学期二模数学(文)试题
3 . 在等腰梯形
中,
为
的中点,将
与
分别沿
向上折起,使
重合于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b201c0b1a56b34d73edd645222957a.png)
![](https://img.xkw.com/dksih/QBM/2021/2/23/2664361924706304/2665212526821376/STEM/bf7ccf6f04dc46db91a3694981ac7993.png?resizew=341)
(1)在折后的三棱锥
中,证明
;
(2)若
,且折后的三棱锥
的表面积是
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb20f88435a11dab092c6e3305b83b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2657e02314469ad2b13d31dce41b4343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a6b28c74741fda4422931730a0131b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b201c0b1a56b34d73edd645222957a.png)
![](https://img.xkw.com/dksih/QBM/2021/2/23/2664361924706304/2665212526821376/STEM/bf7ccf6f04dc46db91a3694981ac7993.png?resizew=341)
(1)在折后的三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4947127020d827801ee2a671bbd86b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85316143e9e86df2ae2c64f0829d1dd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f38a91f5e3218f901f8241a702c72f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4947127020d827801ee2a671bbd86b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4947127020d827801ee2a671bbd86b74.png)
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名校
解题方法
4 . 如图所示,在三棱柱
中,M为棱
的中点.
![](https://img.xkw.com/dksih/QBM/2021/6/14/2742622851866624/2743036705185792/STEM/f83cddb709ab405f8eb506f80a2379a0.png?resizew=241)
(1)求证∶![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
平面
;
(2)若
⊥平面ABC,
,AB=AC=AA1=2,求点B到平面AB1M的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/2021/6/14/2742622851866624/2743036705185792/STEM/f83cddb709ab405f8eb506f80a2379a0.png?resizew=241)
(1)求证∶
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770b4f16694b2bd79a1a93d776a82680.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
您最近一年使用:0次
2021-06-14更新
|
1243次组卷
|
4卷引用:安徽省100名校2020届高三下学期攻疫联考数学(文)试题
安徽省100名校2020届高三下学期攻疫联考数学(文)试题(已下线)考点32 直线、平面平行的判定及其性质-备战2022年高考数学(文)一轮复习考点帮湖北省武汉外国语学校2020-2021学年高一下学期期末数学试题贵州省黔东南自治州镇远县文德民族中学校2022届高三上学期期末数学(文)试题
5 . 如图,BE,CD为圆柱的母线,
是底面圆的内接正三角形,M为BC的中点.
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649543525588992/2650998453493760/EXPLANATION/b94c1d37a7ec4ae6806d679a6d0c9e22.png?resizew=150)
(1)证明:平面AEM⊥平面BCDE;
(2)设BC=BE,圆柱的体积为
,求四棱锥A-BCDE的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649543525588992/2650998453493760/EXPLANATION/b94c1d37a7ec4ae6806d679a6d0c9e22.png?resizew=150)
(1)证明:平面AEM⊥平面BCDE;
(2)设BC=BE,圆柱的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e20dfdb0533931453c63bf22419dbb5.png)
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2021-02-04更新
|
1059次组卷
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8卷引用:安徽省滁州市2020-2021学年高三上学期第一次教学质量监测文科数学试题
安徽省滁州市2020-2021学年高三上学期第一次教学质量监测文科数学试题安徽省马鞍山市2020-2021学年高三上学期第一次教学质量监测文科数学试题(已下线)专题09 立体几何(测)-2021年高考数学二轮复习讲练测(新高考版)(已下线)专题09 立体几何(测)-2021年高考数学二轮复习讲练测(文科)(文理通用)(已下线)专题29 立体几何(解答题)-2021年高考数学(文)二轮复习热点题型精选精练江西省抚州市临川第一中学2021届高三5月模拟考试数学(文)试题宁夏固原市第一中学2021届高三下学期第一次模拟考试数学(文)试题宁夏吴忠中学2022届高三上学期第一次月考数学(文)试题
名校
解题方法
6 . 如图,三棱柱
的各棱的长均为2,
在底面上的射影为
的重心
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/599c6990-7e9a-4530-bd58-a98ab45d1d97.png?resizew=228)
(1)若
为
的中点,求证:
平面
;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/599c6990-7e9a-4530-bd58-a98ab45d1d97.png?resizew=228)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07391ef575d28f09bc5cda0ff8130a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2213b575a7cfaffcdf91885005c7d.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcd4aa8e2e84c4605a84097167e216a.png)
您最近一年使用:0次
2021-02-03更新
|
1527次组卷
|
2卷引用:安徽省芜湖市2020-2021学年高三上学期期末文科数学试题
解题方法
7 . 已知正方体
,棱长为2,
为棱
的中点,
为面对角线
的中点,如下图.
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646446661935104/2647522973016064/STEM/f2c4185af67545d6a9a951eb7461da2e.png?resizew=340)
(1)求三棱锥
的体积;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646446661935104/2647522973016064/STEM/f2c4185af67545d6a9a951eb7461da2e.png?resizew=340)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d25c7142882b573eb4db8286e4b1a9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4196374b64beb85418d3a1c66fc772b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad6b3d073d8dd1cb7d9c89116b9d81.png)
您最近一年使用:0次
解题方法
8 . 如图1,边长为4的正方形
中,点E,F分别是边
,
的中点,将
,
分别沿
,
折起,使A,C两点重合于点P如图2.设
与
交于点O.
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645223176323072/2646094153474048/STEM/d2353ffd88db4d039cadd9b08e033124.png?resizew=348)
(1)求证:
平面
;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c771a4feb150ad9cff8d70431c97eb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13668f033d00acfc366f7e47949c4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645223176323072/2646094153474048/STEM/d2353ffd88db4d039cadd9b08e033124.png?resizew=348)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357f2bfe607af1cdef85dfc603e3192f.png)
您最近一年使用:0次
名校
解题方法
9 . 如图所示,ABCD是正方形,O是正方形的中心,PO⊥底面ABCD,底面边长为a,E是PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/a0126330-7a6f-45ea-a898-c68b3e88478d.png?resizew=172)
(1)求证:PA∥平面BDE;
(2)平面PAC⊥平面BDE;
(3)若二面角E﹣BD﹣C为30°,求四棱锥P﹣ABCD的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/a0126330-7a6f-45ea-a898-c68b3e88478d.png?resizew=172)
(1)求证:PA∥平面BDE;
(2)平面PAC⊥平面BDE;
(3)若二面角E﹣BD﹣C为30°,求四棱锥P﹣ABCD的体积.
您最近一年使用:0次
2022-06-14更新
|
1529次组卷
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12卷引用:安徽省池州市第一中学2020-2021学年高二上学期期中数学(文)试题
安徽省池州市第一中学2020-2021学年高二上学期期中数学(文)试题【全国百强校】湖南师范大学附属中学2017-2018学年高一上学期期末考试数学试题(已下线)第02章 章末检测(A)-2018-2019版数学创新设计课堂讲义同步系列(人教A版必修2)湖南省衡阳市衡阳县第四中学2019-2020学年高一(菁华班)上学期期中A卷数学试题河北省张家口市第一中学(普通实验班)2020-2021学年高二上学期10月月考数学试题广东省佛山市顺德区第一中学2019-2020学年高二上学期第一次阶段考试数学试题(已下线)专题25 二面角相关问题训练-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)宁夏银川唐徕回民中学2021-2022学年高一下学期期末考试数学试题(已下线)专题23 空间中的垂直关系(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)甘肃省张掖市某重点校2022-2023学年高一下学期6月月考数学试题湖南省株洲市炎陵县2022-2023学年高二下学期期末数学试题黑龙江省龙西北八校联合体2022-2023学年高一下学期期末考试数学试题
解题方法
10 . 某几何体的三视图如图所示,求该几何体的表面积和体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/da3a04ab-6e3d-49ce-87e7-e31175249d4a.png?resizew=177)
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