名校
解题方法
1 . 如图正方体
的棱长为2,
是线段
的中点,平面
过点
.
截正方体所得的截面,并简要叙述理由或作图步骤;
(2)求(1)中截面多边形的面积;
(3)平面
截正方体,把正方体分为两部分,求较小的部分与较大的部分的体积的比值.
![](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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e5eadee90c7863040cd6889ad8b4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)求(1)中截面多边形的面积;
(3)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2024-05-04更新
|
494次组卷
|
5卷引用:第六章立体几何初步章末二十种常考题型归类(1)-【帮课堂】(北师大版2019必修第二册)
(已下线)第六章立体几何初步章末二十种常考题型归类(1)-【帮课堂】(北师大版2019必修第二册)河北省文安县第一中学2023-2024学年高一清北班下学期3月月考数学试卷江苏省无锡市辅仁高级中学2023-2024学年高一下学期期中考试数学试题四川省广安第二中学校2023-2024学年高一下学期第二次月考数学试题江苏省无锡市辅仁高级中学2023-2024学年高二下学期期中考试数学试题
名校
解题方法
2 . 如图,棱长为
的正方体
,点
分别在棱
上,过点
的截面将正方体分割成两部分.
的平面与正方体表面的交线;(无需证明,保留作图痕迹);
(2)若点
分别为
中点,求过点
的截面将正方体分割的较小部分几何体的体积.
![](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/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3472985d11e56d62b88cc8c5ac25fd82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3472985d11e56d62b88cc8c5ac25fd82.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3472985d11e56d62b88cc8c5ac25fd82.png)
您最近一年使用:0次
2023-06-21更新
|
618次组卷
|
6卷引用:8.3.1棱柱、棱锥、棱台的表面积和体积(分层作业)-【上好课】
(已下线)8.3.1棱柱、棱锥、棱台的表面积和体积(分层作业)-【上好课】(已下线)11.1空间几何体-同步精品课堂(人教B版2019必修第四册)辽宁省六校2022-2023学年高一下学期6月联考数学试题辽宁省六校协作体2022-2023学年高一下学期第三次考试(6月)数学试题陕西省西安市铁一中学国际部2023-2024学年高一下学期第三月考数学试题河南省开封市五县联考2023-2024学年高一下学期第二次月考数学试题
名校
解题方法
3 . 如图1所示,在边长为3的正方形
中,将
沿
折到
的位置,使得平面
平面
,得到图2所示的三棱锥
.点
分别在
上,且
,
,
.记平面
与平面
的交线为l.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/a232b33a-64b7-48ee-ad75-468ec615404d.png?resizew=335)
(1)在图2中画出交线l,保留作图痕迹,并写出画法.
(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/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1095b030f441de5fb223781b00f3dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bb1063e139610045f3bca5ca0b2766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715ef932b72eb703f3e7a17ee2ce6a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828795d52174dd64fba1c9ebe61072b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cf0ee918f8c2f753302d3b5928d358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/a232b33a-64b7-48ee-ad75-468ec615404d.png?resizew=335)
(1)在图2中画出交线l,保留作图痕迹,并写出画法.
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7f9eca6d2aabe3f9e0f39b46106ce4.png)
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2023-04-25更新
|
509次组卷
|
3卷引用:重难点12 立体几何必考经典解答题全归类【九大题型】
名校
解题方法
4 . 已知四棱锥
的底面
是平行四边形,侧棱
平面
,点
在棱
上,且
,点
是在棱
上的动点(不为端点).(如图所示)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/3113b3d8-5a6b-4eda-8791-3d3b71470c49.png?resizew=183)
(1)若
是棱
中点,
(i)画出
的重心
(保留作图痕迹),指出点
与线段
的关系,并说明理由;
(ii)求证:
平面
;
(2)若四边形
是正方形,且
,当点
在何处时,直线
与平面
所成角的正弦值取最大值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85ce5e111acf7162b8e1b5a3f6b220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/3113b3d8-5a6b-4eda-8791-3d3b71470c49.png?resizew=183)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(i)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.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/f50b3ae183997b707d16eb4e7f6712fa.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf2bc3dd1f1ae5d5e28b0366f454ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2304c541406034dd83040e9a7887ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
您最近一年使用:0次
2023-02-11更新
|
710次组卷
|
3卷引用:重难点突破06 立体几何解答题最全归纳总结(九大题型)-2
(已下线)重难点突破06 立体几何解答题最全归纳总结(九大题型)-2广东省汕头金中、湛江一中、东莞东华、广州六中四校2023届高三下学期联考数学试题四川省绵阳南山中学实验学校2023届高三补习班下学期2月考试考试理科数学试题
名校
解题方法
5 . 如图所示,正方体
的棱长为a.
的顶点
,B,
截下一个三棱锥
,求正方体剩余部分的体积;
(2)若M,N分别是棱AB,BC的中点,请画出过
,M,N三点的平面与正方体
表面的交线(保留作图痕迹,画出交线,无需说明理由),并求出交线围成的多边形的周长;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdaa8065bea92fe61bce56090d8cb235.png)
(2)若M,N分别是棱AB,BC的中点,请画出过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
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名校
6 . 在
中,角
所对边分别为
,若
.
(1)证明:
为等边三角形;
(2)若(1)中的等边
边长为2,试用斜二测法画出其直观图,并求直观图面积.
注:只需画出直观图并求面积,不用写出详细的作图步骤.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec3f79448524d6848be51fdd5c7a150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1b5305cb9b5a90c4f13bceaaee4fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8176a512a8e931c56d85607764f48851.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若(1)中的等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
注:只需画出直观图并求面积,不用写出详细的作图步骤.
您最近一年使用:0次
2023高一·全国·专题练习
7 . 已知四棱锥
中,底面
为直角梯形,
平面
,
,
,
,
,M为
中点,过C,D,M的平面截四棱锥
所得的截面为
.若
与棱
交于点F,画出截面
,保留作图痕迹(不用说明理由),求点F的位置;
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef699f5dc072b853cfe700c6f1abbbae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2753753faf2cb9a0003aa8e3945159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80137ee8af4684ce558242d8b3f1459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/b33672a1-1c35-447a-87ee-0fa74e5ecb5f.png?resizew=156)
您最近一年使用:0次
解题方法
8 . 已知四棱锥
中,底面
为直角梯形,
平面
,
,
,
,
,M为
中点,过C,D,M的平面截四棱锥
所得的截面为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/38a4abaf-0a39-4e83-ace1-0120f4ff5f14.png?resizew=155)
(1)若
与棱
交于点F,画出截面
,保留作图痕迹(不用说明理由),求点F的位置;
(2)求平面
与平面
所成锐二面角的余弦值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceb5cc71fc50f20649f6b9535fd914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2753753faf2cb9a0003aa8e3945159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80137ee8af4684ce558242d8b3f1459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/38a4abaf-0a39-4e83-ace1-0120f4ff5f14.png?resizew=155)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe67036b4671b5d2a5c55b48c4d3bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,正方体
中,M,N,E,F分别是
,
,
,
的中点.
(2)求证:平面
平面EFDB;
(3)画出平面BNF与正方体侧面的交线
需要有必要的作图说明、保留作图痕迹,并说明理由
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46f725fb1c57d0855a0a6cc26bf562a.png)
(3)画出平面BNF与正方体侧面的交线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce08128582a7e855852c03e0ac5d0487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8c94316312f093ebfc80b872a83c25.png)
您最近一年使用:0次
名校
解题方法
10 . 图形是信息传播、互通的重要的视觉语言《画法几何》是法国著名数学家蒙日的数学巨著,该书在投影的基础上,用“三视图”来表示三维空间中立体图形.其体来说.做一个几何的“三视图”,需要观测者分别从几何体正面、左面、上面三个不同角度观察,从正投影的角度作图.下图中粗实线画出的是某三棱锥的三视图,且网格纸上小正方形的边长为1,则该三棱锥的外接球的表面积为( )
![](https://img.xkw.com/dksih/QBM/2022/4/7/2953094975799296/2953733587304448/STEM/1a7ca7a8908e4a54b8f65ca0b59d6346.png?resizew=474)
![](https://img.xkw.com/dksih/QBM/2022/4/7/2953094975799296/2953733587304448/STEM/1a7ca7a8908e4a54b8f65ca0b59d6346.png?resizew=474)
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2022-04-08更新
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8卷引用:理科数学-2022年高考押题预测卷01(全国甲卷)
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