名校
解题方法
1 . 如图,在四棱柱
中,侧棱
垂直底面
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4adb74be3d8886525bc02bbc2f0f556.png)
(1)求证: CD⊥平面
.
(2)已知
,求二面角
的大小.
(3)现将与四棱柱
形状和大小完全相同的两个四棱柱拼成一个新的四棱柱,规定:若拼成的新四棱柱形状和大小完全相同,则视为同一种拼接方案,问共有几种不同的拼接方案?在这些拼接成的新四棱柱中,记其中最小的表面积为
,写出
的解析式.(直接写出答案,不必说明理由)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4adb74be3d8886525bc02bbc2f0f556.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/9/cab0c144-a341-47af-911d-2805d8a96701.png?resizew=160)
(1)求证: CD⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3fec4fba64d1631538fb9da2c846e23.png)
(3)现将与四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e6cb8d4e39fa44f71df04b74f123f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e6cb8d4e39fa44f71df04b74f123f4.png)
您最近一年使用:0次
14-15高二上·浙江嘉兴·阶段练习
2 . 有两个相同的直三棱柱,高为
,底面三角形的三边长分别为
,
,
,用它们拼成一个三棱柱或四棱柱,在所有可能的情形中,全面积最小的是一个三棱柱,则
的取值范围是__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfe017e21d1a4e5cf7b1fbf44fcc0ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2a7b13d95229e2e938514739054541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182841875763d3ce72c6ad0bc7183869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-02-28更新
|
1354次组卷
|
17卷引用:2014-2015学年浙江省嘉兴市一中高二上学期第一次阶段测试数学试卷
(已下线)2014-2015学年浙江省嘉兴市一中高二上学期第一次阶段测试数学试卷上海市曹杨第二中学2018-2019学年高二上学期期末复习试卷1数学试题上海市金山区亭林中学2020-2021学年高二下学期期末数学试题沪教版(2020) 必修第三册 新课改一课一练 期中测试A上海市崇明区2021-2022学年高二上学期期末数学试题上海市第六十中学2021-2022学年高二上学期期中数学试题上海市向明中学2021-2022学年高二上学期期中数学试题(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)11.1 柱体(第2课时)(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)上海市闵行(文琦)中学2023-2024学年高二下学期3月月考数学试题2005年普通高等学校招生考试数学(文)试题(上海卷)2005年普通高等学校招生考试数学(理)试题(上海卷)(已下线)第23练 几何体的体积与表面积山东省菏泽市定陶区明德学校(山大附中实验学校)2022-2023学年高一(创新部)下学期6月月考数学试题(已下线)8.3简单几何体的表面积与体积【第三课】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)8.3.1 棱柱、棱锥、棱台的表面积和体积-同步精品课堂(人教A版2019必修第二册)
名校
3 . 三棱柱
中,
,点
是
的外心,
平面
,
,二面角
为
,则下列选项中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd8f940b796af67206b3f9dd410a407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1654dfe63f11563eadbaee32dae7b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
A.三棱柱的侧面积为![]() |
B.![]() ![]() ![]() |
C.点![]() ![]() ![]() |
D.若四棱锥![]() ![]() |
您最近一年使用:0次
2023-01-16更新
|
763次组卷
|
3卷引用:安徽省涡阳第四中学2022-2023学年高二下学期第二次月考数学试题
名校
解题方法
4 . 如图,三棱柱
中,侧面
为菱形,
的中点为
,且
平面
.
;
(2)若
,
,
,求三棱柱
的高;
(3)在(2)的条件下,求三棱柱
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db87b41df9d3c83d2810a4265d768d3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7fd49bb962841b4575805030e19add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e238b2757353026133bbe495645e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(3)在(2)的条件下,求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
您最近一年使用:0次
2022-09-15更新
|
1404次组卷
|
5卷引用:湖南省常德市汉寿县第一中学2022-2023学年高二下学期开学考试数学试题
湖南省常德市汉寿县第一中学2022-2023学年高二下学期开学考试数学试题沪教版(2020) 必修第三册 经典导学 期中测评(已下线)高考新题型-立体几何初步(已下线)第29讲 线面垂直证线线平行和垂直2种题型(已下线)专题8.15 空间中线面的位置关系大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
名校
解题方法
5 . 如图,在三棱锥
中,
,
,
,
为
的中点,点
是棱
上一动点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/5/3/2971556730806272/2973106767036416/STEM/6a23df76-c75c-4356-94a4-f8d00530a460.png?resizew=219)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4957406b21df59fdf7fa184752287b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1082dd7e08556354aa7d4861d419e4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b4c1ae9c57d51e27bbdb001122d3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/5/3/2971556730806272/2973106767036416/STEM/6a23df76-c75c-4356-94a4-f8d00530a460.png?resizew=219)
A.三棱锥![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2022-05-05更新
|
1009次组卷
|
4卷引用:辽宁省东北育才学校科学高中部2023-2024学年高二上学期第一次月考数学试题
名校
6 . 如图,在直四棱柱
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b05db872c7a37e0d06ca9f0278f9562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f8caf1d83ac27191a7a4ce3d81c769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5fb45af7400c71ac728f9dfa09a5cb.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d30832deeebfc30b1799624e75b75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223036d27be5914db50fbd5cb19d4212.png)
:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/727ef02f-bf3c-4f85-8b52-52dc0d6654f1.png?resizew=182)
(1)求证:
平面
;
(2)现将与四棱柱
形状和大小完全相同的两个四棱柱拼成一个新的四棱柱,规定:若拼成的新四棱柱形状和大小完全相同,则视为同一种拼接方案,问共有几种不同的拼接方案?在这些拼接成的新四棱柱中,记其中最小的表面积为
,写出
的解析式;(直接写出答案,不必说明理由)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b05db872c7a37e0d06ca9f0278f9562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f8caf1d83ac27191a7a4ce3d81c769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5fb45af7400c71ac728f9dfa09a5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5cab760038d20eac10fe6108fbb334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d30832deeebfc30b1799624e75b75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223036d27be5914db50fbd5cb19d4212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b377f632949bff36083a5464113387fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/727ef02f-bf3c-4f85-8b52-52dc0d6654f1.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)现将与四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e6cb8d4e39fa44f71df04b74f123f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e6cb8d4e39fa44f71df04b74f123f4.png)
您最近一年使用:0次
名校
7 . 如果一个正四棱柱与一个圆柱的体积相等,那么我们称它们是一对:“等积四棱圆柱”.将“等积四棱圆柱”的正四棱柱,圆柱的表面积与高分别记为
与
.
(1)若
,求
的值.
(2)若
,求证:
;
(3)求实数
的取值范围,使得存在一对“等积四棱圆柱”,满足
与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2872c7017fa524f541698be177ec80c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b49cf76b4f6badb0e6bbe222ad84e5d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c1db3caa89156f2cd0e74393a5895e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84f27e920fe12854e85c6aa2533a8bf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e25402540142dc030c0666839fc7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79dc44b2fafa2b4e6ba0cd543302bfa0.png)
(3)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbaf18914596f229d15f9811d1d6edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae4185929825f622b1b8b396af51f38.png)
您最近一年使用:0次
8 . 某几何体的三视图如图所示,则该几何体的表面积为
![](https://img.xkw.com/dksih/QBM/2017/5/8/1682702594457600/1683310842142720/STEM/44fbdaadd4914d2680b48e2544eebf51.png?resizew=235)
![](https://img.xkw.com/dksih/QBM/2017/5/8/1682702594457600/1683310842142720/STEM/86bc3a009ad04c2caf7709c58320dcce.png?resizew=108)
![](https://img.xkw.com/dksih/QBM/2017/5/8/1682702594457600/1683310842142720/STEM/44fbdaadd4914d2680b48e2544eebf51.png?resizew=235)
![](https://img.xkw.com/dksih/QBM/2017/5/8/1682702594457600/1683310842142720/STEM/86bc3a009ad04c2caf7709c58320dcce.png?resizew=108)
A.![]() | B.![]() | C.![]() | D.![]() |
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