解题方法
1 . 如图,在斜三棱柱
中,
,且三棱锥
的体积为
.
(1)求三棱柱
的高;
(2)若平面
平面
为锐角,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131b887a0a088c760df5e17bd93bfe6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/b7376265-a332-4131-9844-0dccb3b38662.png?resizew=168)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1111386161dc558c54930e35aa302737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bbdf5dbf9df96742624ada95c36146.png)
您最近一年使用:0次
2024-02-24更新
|
222次组卷
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4卷引用:河南省焦作市2023-2024学年高二上学期1月期末考试数学试题
2 . 如图,四棱锥的底面
是边长为
的菱形,
,
,
,平面
平面
,E,F分别为
,
的中点.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
您最近一年使用:0次
2023-11-07更新
|
620次组卷
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5卷引用:河南省焦作市博爱县第一中学2023-2024学年高二上学期期中数学试题
名校
解题方法
3 . 已知直棱柱
的底面ABCD为菱形,且
,
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/bf4f4ba7-42b3-42a0-8813-ce7348d4c82c.png?resizew=206)
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ac37630bf01a67dab22f61ce6e726a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/bf4f4ba7-42b3-42a0-8813-ce7348d4c82c.png?resizew=206)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e106d67ff8828b5fb9165de66ea28da7.png)
您最近一年使用:0次
2023-03-04更新
|
1249次组卷
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9卷引用:河南省焦作市博爱县第一中学2022-2023学年高二下学期4月月考数学试题
河南省焦作市博爱县第一中学2022-2023学年高二下学期4月月考数学试题四川省内江市第六中学2022-2023学年高二下学期第一次月考数学(文科)试题江西省南昌市2023届高三第一次模拟测试数学(文)试题(已下线)期中考试测试(基础)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)专题13立体几何(解答题)(已下线)立体几何专题:空间几何体体积的5种题型(已下线)专题20 空间几何解答题(文科)-2山东省滕州市第五中学2022-2023学年高一下学期5月月考数学试题河北省石家庄师大附中2022-2023学年高一下学期第三次月考数学试题
解题方法
4 . 在如图所示的几何体
中,
底面
,底面
是边长为4的正方形,其中心为P,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/42562408-3414-4b7d-babd-47f920f365fa.png?resizew=195)
(1)求三棱锥
的体积;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fc1129846f37afdafd751627c450d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd3bc5c12b7f2e3974daf5d129f8b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b70c03f14f9f5c55c5b8d536437b90.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/42562408-3414-4b7d-babd-47f920f365fa.png?resizew=195)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437c9774700f6c066b3e19d17d54b368.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c9c2c831a0552a7c934365bc49ad3f.png)
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名校
5 . 如图,多面体
中,
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0ae57ea3922dd4d1493a4a8e040995.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b4fbd5a6-8069-4979-a39e-66b633f7572e.png?resizew=153)
(1)在线段
上是否存在一点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
平面
?如果存在,请指出
点位置并证明;如果不存在,请说明理由;
(2)当三棱锥
的体积为8时,求平面
与平面AFC夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8df226cdfaf59a111f778ce07d33d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee21949feefb980c0d65587ff0497d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0ae57ea3922dd4d1493a4a8e040995.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b4fbd5a6-8069-4979-a39e-66b633f7572e.png?resizew=153)
(1)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a0d238b6e9b49bbea22a79402e8e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e024a87e5b48bfa241169def613104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29319a28b4ab8cc3a20f0673fd0c24c0.png)
您最近一年使用:0次
2022-05-31更新
|
1652次组卷
|
5卷引用:河南省焦作市博爱县第一中学2023-2024学年高二上学期期中数学试题
6 . 如图所示,在四棱柱
中,底面
是菱形,
.
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844837721964544/2845017587367936/STEM/539f5d39-a074-4603-9db1-a3c087837d14.png?resizew=235)
(1)证明:平面
平面
;
(2)若四边形
是正方形,
,求四棱柱
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e735911ba4cd7f8fca6b3f65d705b573.png)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844837721964544/2845017587367936/STEM/539f5d39-a074-4603-9db1-a3c087837d14.png?resizew=235)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a05e0ab55e325fb3b85fc8ca9c27c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
2021-11-05更新
|
191次组卷
|
3卷引用:河南省焦作市普通高中2021-2022学年高二上学期期中考试文科数学试题
河南省焦作市普通高中2021-2022学年高二上学期期中考试文科数学试题河南省焦作市普通高中2021-2022学年高二上学期期中数学理科试题(已下线)上海市静安区2023届高三二模数学试题变式题16-21
名校
解题方法
7 . 如图1,圆O的半径为2,
均为该圆的直径,弦
垂直平分半径
,垂足为F,沿直径
将半圆
所在平面折起,使两个半圆所在的平面互相垂直(如图2).
![](https://img.xkw.com/dksih/QBM/2021/9/13/2807143142916096/2810595185229824/STEM/0d27930f-5bd5-4c3f-8d3c-a1642003df2d.png?resizew=548)
(1)求
的积;
(2)如图2,在劣弧
上是否存在一点P(异于
两点),使得
平面
?若存在,请加以证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a9a6d8dc376ca4c4aa7c8a4ee1aee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf468f5132e14ee1d8cc766808b11af.png)
![](https://img.xkw.com/dksih/QBM/2021/9/13/2807143142916096/2810595185229824/STEM/0d27930f-5bd5-4c3f-8d3c-a1642003df2d.png?resizew=548)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799f7979ac1aaf08e24117bb9f4690f5.png)
(2)如图2,在劣弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2cedc7e41872c652fc4f2d619e5550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bc5d8308a060d6068cfc9f69fe79e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20bea1a042a5c5e63cad31714fc67b66.png)
您最近一年使用:0次
2021-09-18更新
|
313次组卷
|
4卷引用:河南省焦作市温县第一高级中学2021-2022学年高二上学期10月月考数学(理)试题
名校
解题方法
8 . 已知四边形
满足
,
,
是
的中点,将
沿着
翻折成
,使平面
平面
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/8/28/2796010114875392/2796655518752768/STEM/6a9a275a-92d5-47a6-86f3-91392e450585.png?resizew=408)
(1)求四棱锥
的体积;
(2)求平面
与平面
所成角的正弦值.
![](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/da7bcefad703f1ce4458f698a8bd6267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09a769a75b107390b9eeccc929f761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f38a857b9fabe179c565feb88de4175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c60a0de546f75b46348265746aa707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://img.xkw.com/dksih/QBM/2021/8/28/2796010114875392/2796655518752768/STEM/6a9a275a-92d5-47a6-86f3-91392e450585.png?resizew=408)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72dfcc26700f0801e8113e1caeb4a6eb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2213b575a7cfaffcdf91885005c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d970ac0eac1ba7a0e91c5c755e6a6980.png)
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2021-08-29更新
|
498次组卷
|
4卷引用:河南省焦作市宇华实验学校2023-2024学年高二上学期宏志班第二次月考数学试题
名校
解题方法
9 . 如图,已知四棱锥
中,
分别是
的中点,
底面
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5409942c6a29b7f347e22ed656e4d1b3.png)
![](https://img.xkw.com/dksih/QBM/2021/5/11/2718965672411136/2720728923897856/STEM/e130e9f364104801bde24b28b84e692d.png?resizew=224)
(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/a8a3842f9e99b71d9fc4baa9c471a3da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd5e413cb380bfad5af472412236775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5409942c6a29b7f347e22ed656e4d1b3.png)
![](https://img.xkw.com/dksih/QBM/2021/5/11/2718965672411136/2720728923897856/STEM/e130e9f364104801bde24b28b84e692d.png?resizew=224)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345368a256c743818a7ca1487ae4c4f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b5e0b8c35a7d9b3d68db8e5c89b8bd.png)
您最近一年使用:0次
2021-05-14更新
|
1210次组卷
|
6卷引用:河南省温县第一高级中学2021-2022学年高二下学期3月月考文科数学试题
名校
解题方法
10 . 如图是矩形
和以边
为直径的半圆组成的平面图形,
.将此图形沿
折叠,使平面
垂直于半圆所在的平面.若点E是折后图形中半圆O上异于A,B的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/08466985-cf10-48a3-ace0-2eff8fd6630c.png?resizew=334)
(Ⅰ)证明:
;
(Ⅱ)若异面直线
和
所成的角为
,求三棱锥
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/d45187cdeb695ced04c4736583520d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/08466985-cf10-48a3-ace0-2eff8fd6630c.png?resizew=334)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad2dc5dea4563dfd9afefeb8b210eeb.png)
(Ⅱ)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade68d3f913ba0357f38a808392f5820.png)
您最近一年使用:0次
2021-05-12更新
|
671次组卷
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5卷引用:河南省沁阳市第一中学2020-2021学年高二下学期密集训练(三)数学(文)试题