名校
解题方法
1 . 如图,在棱长为
的正方体
中,
为棱
的中点,
,
分别是棱
,
上的动点(不与顶点重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/7230b3f9-55f8-4ce6-9945-25efc93a341a.png?resizew=180)
(1)作出平面
与平面
的交线(要求写出作图过程),并证明:若平面
平面
,则
;
(2)若
,
均为其所在棱的中点,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/7230b3f9-55f8-4ce6-9945-25efc93a341a.png?resizew=180)
(1)作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abb06405623edb5c9d5f7350d79dc76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8b5a6dbcf05f572f83f51abf7d668c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ecd2020a3f7767e54ab47e640399a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c6b8443e6525024643e9d87c45640f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
您最近一年使用:0次
解题方法
2 . 已知ABCD是边长为2的正方形,平面
平面DEC,直线AE,BE与平面DEC所成的角都为45°.
![](https://img.xkw.com/dksih/QBM/2021/11/18/2854152125972480/2861941634793472/STEM/2c0f360e744247acbdc48ea7ad5bfe81.png?resizew=214)
(1)证明:
.
(2)求四棱锥E-ABCD的体积V.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://img.xkw.com/dksih/QBM/2021/11/18/2854152125972480/2861941634793472/STEM/2c0f360e744247acbdc48ea7ad5bfe81.png?resizew=214)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0aaa5cf7dafac1b64eafe84cae5674.png)
(2)求四棱锥E-ABCD的体积V.
您最近一年使用:0次
2021-11-29更新
|
315次组卷
|
2卷引用:贵州省毕节市金沙县2022届高三11月月考数学(文)试题
解题方法
3 . 已知四边形ABCD是边长为2的正方形,平面
平面DEC,且
,平面ADE与平面BEC所成的锐二面角为60°.
![](https://img.xkw.com/dksih/QBM/2021/11/18/2854138359078912/2861236373798912/STEM/bb6bec76-c996-44ea-b03b-5001a5b13ce2.png?resizew=158)
(1)求四棱锥
的体积;
(2)当四棱锥
的体积大于1时,求直线EC与平面ABE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b506c24f554901249694f21d9621b23.png)
![](https://img.xkw.com/dksih/QBM/2021/11/18/2854138359078912/2861236373798912/STEM/bb6bec76-c996-44ea-b03b-5001a5b13ce2.png?resizew=158)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
(2)当四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
您最近一年使用:0次
2021-11-28更新
|
157次组卷
|
2卷引用:贵州省毕节市金沙县2022届高三11月月考数学(理)试题
名校
解题方法
4 . 已知菱形
的边长为
,
,如图1.沿对角线
将
向上折起至
,连接
,构成一个四面体
,如图2.
;
(2)若
,求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c967c9b3f669ea78edd838e1d8b59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685534ba47e83433200ce29660875118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
您最近一年使用:0次
2021-11-13更新
|
1017次组卷
|
7卷引用:贵州省贵州师范大学附属中学2021-2022学年高二10月月考数学(理)试题
名校
解题方法
5 . 如图所示,在三棱锥
中,
是边长为
的正三角形,
点在平面
的正投影
是
的中心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/209333d9-47ed-479c-bf50-8efc9711a2a0.png?resizew=176)
(1)求证:
;
(2)若点
到平面
的距离为
,求此三棱锥的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/209333d9-47ed-479c-bf50-8efc9711a2a0.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38be38165dc2307982fc57001a447c56.png)
您最近一年使用:0次
2021-11-13更新
|
259次组卷
|
2卷引用:贵州省凯里市第一中学2021-2022学年高二上学期期中考试数学(文)试题
6 . 如图,已知多面体
的底面
是边长为2的菱形,
,
是等边三角形,且平面
底面
底面
.
![](https://img.xkw.com/dksih/QBM/2021/10/21/2834276079591424/2836816913178624/STEM/0c98971b-0a46-4279-b3ea-09e5ea038599.png?resizew=293)
(1)在平面
内找到一个点G,使得
,只需说明作法即可,不必说明理由;
(2)求(1)中确定点G到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e90f9f4e44173888a54c624852064a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681d6dac52a0d530ab5ae8fff6912b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a677563f41e105ef2d85e7fa9ca551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbc268139159c5a094e14e35eb3342e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade75694e46d62685d8be1973b893235.png)
![](https://img.xkw.com/dksih/QBM/2021/10/21/2834276079591424/2836816913178624/STEM/0c98971b-0a46-4279-b3ea-09e5ea038599.png?resizew=293)
(1)在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a62e5d07ecb42e0fa39213092eb4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9982c4731e7a7a86ba47370c856fb312.png)
(2)求(1)中确定点G到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e51817ee1ebf17c73ed21171bcfc5b5.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在四棱锥
中,底面ABCD是矩形,
平面
,
分别是PB、CD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/3be02aa5-8455-4e0e-851e-82c7447c4359.png?resizew=183)
(1)证明:
平面PAD;
(2)若
平面AEF,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6960c860029299cbca5a0bdd6e9497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524d117abd8ca0e77c084981dd1a1fbe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/3be02aa5-8455-4e0e-851e-82c7447c4359.png?resizew=183)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd108b4303ba28bd8d1ad99380a9a621.png)
您最近一年使用:0次
2021-10-05更新
|
515次组卷
|
5卷引用:贵州省黔西南州兴义市顶效开发区顶兴学校2022-2023学年高一下学期期中考试数学试题
8 . 如图,圆锥的底面直径和高均是4,过
的中点
作平行于底面的截面,以该截面为底面挖去一个圆柱,
![](https://img.xkw.com/dksih/QBM/2021/9/30/2819323673427968/2822745480011776/STEM/7ac2cb751a2a4c329272411897b8ce67.png?resizew=143)
(1)求剩余几何体的体积
(2)求剩余几何体的表面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://img.xkw.com/dksih/QBM/2021/9/30/2819323673427968/2822745480011776/STEM/7ac2cb751a2a4c329272411897b8ce67.png?resizew=143)
(1)求剩余几何体的体积
(2)求剩余几何体的表面积
您最近一年使用:0次
2021-10-05更新
|
380次组卷
|
4卷引用:贵州省遵义市新蒲新区2021-2022学年高二上学期期中联考数学试题
9 . 如图,在四棱锥
中,底面
是边长为2的正方形,平面
底面
,
.
![](https://img.xkw.com/dksih/QBM/2021/9/26/2816226581807104/2820781153599488/STEM/5951a97994b348808eede14a7cdec8f4.png?resizew=192)
(1)证明:平面
平面
;
(2)已知点
是线段
的中点,求点
到平面
的距离,
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36bd3b2701a86536663fbe6b65a7c61.png)
![](https://img.xkw.com/dksih/QBM/2021/9/26/2816226581807104/2820781153599488/STEM/5951a97994b348808eede14a7cdec8f4.png?resizew=192)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03203dd5ac79dd8c6707e4340773359.png)
您最近一年使用:0次
解题方法
10 . 如图,在四面体PABC中,△ABC为等边三角形,PA=AB=2,PB=PC=2
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/929e9681-c6f0-4e26-95af-fd7e87c420e7.png?resizew=136)
(1)证明:BC⊥PA.
(2)若D为棱BC的中点,Q为棱PC上一点,且PQ=2QC,求三棱锥Q-ABD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/929e9681-c6f0-4e26-95af-fd7e87c420e7.png?resizew=136)
(1)证明:BC⊥PA.
(2)若D为棱BC的中点,Q为棱PC上一点,且PQ=2QC,求三棱锥Q-ABD的体积.
您最近一年使用:0次