2023·全国·模拟预测
解题方法
1 . 如图,多面体
中,
为正三角形,
,平面
平面
平面
.
(1)求证:
;
(2)求该多面体的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb13525ba2f601e237b86017a98b13f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4d4921c8a8186dae66ba5b0230c61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60519f44e3007a192566e5a7b00f791d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea54a8278bb8ee6482a728e0fe04ed8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/b5a1fd99-afbe-4e88-b6ed-f603691409b6.png?resizew=173)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c847ae3dc08249be7d9904b539b58980.png)
(2)求该多面体的表面积.
您最近一年使用:0次
解题方法
2 . 如图,该几何体是由圆柱和三棱锥
组合而成的,四边形
为轴截面,
是圆
的直径,
平面
.
(1)求证:
垂直
所确定的平面.
(2)求该几何体的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a9efd1901bd29dc04f6a5335b15d9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/24/efb0e42a-0b51-4fb5-b873-3c12f58ff3db.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2fb188915d2e3d7bfd633fa18221b07.png)
(2)求该几何体的表面积.
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名校
解题方法
3 . 已知直三棱柱
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/12/7/2867393608392704/2868877442506752/STEM/2dbb6858e68946e48247a7cc5cf2d1ec.png?resizew=132)
![](https://img.xkw.com/dksih/QBM/2021/12/7/2867393608392704/2868877442506752/STEM/7c2832dd27a5462f951b507436e5590f.png?resizew=223)
(1)若
为
的中点,证明:
平面
;
(2)将两块形状与该直三棱柱完全相同的木料按如图所示两种方案沿阴影面进行分割,把木料一分为二,留下体积较大的一块木料.根据你所学的知识,请判断采用哪一种方案会使留下的木料表面积较大,并求出这个较大的表面积和说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6baf49925a5bcb359b542d45067c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://img.xkw.com/dksih/QBM/2021/12/7/2867393608392704/2868877442506752/STEM/2dbb6858e68946e48247a7cc5cf2d1ec.png?resizew=132)
![](https://img.xkw.com/dksih/QBM/2021/12/7/2867393608392704/2868877442506752/STEM/7c2832dd27a5462f951b507436e5590f.png?resizew=223)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a4b438e2e6687c7cd55ea08bbaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb7e8ef610cb5588bd52755399921a.png)
(2)将两块形状与该直三棱柱完全相同的木料按如图所示两种方案沿阴影面进行分割,把木料一分为二,留下体积较大的一块木料.根据你所学的知识,请判断采用哪一种方案会使留下的木料表面积较大,并求出这个较大的表面积和说明理由.
您最近一年使用:0次
名校
解题方法
4 . 已知长方体
中,
,点
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2020/12/23/2620466755870720/2623358836056064/STEM/20f492a1-c302-4ff0-a97d-481efecf06fb.png)
(1)若点
在直线
上运动,求证:
;
(2)如图所示,若
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e44924029eade339e7e5f8af499ad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2020/12/23/2620466755870720/2623358836056064/STEM/20f492a1-c302-4ff0-a97d-481efecf06fb.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5cc20109a6aa69219b1f58cea5182db.png)
(2)如图所示,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b046cc9fd06e3a24f4b99c3ab14a98d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9340ff2654b3db87bee2a74df881415.png)
您最近一年使用:0次
2020-12-27更新
|
150次组卷
|
3卷引用:江西省重点中学2021届高三上学期总复习阶段性检测考试数学(文)试题
名校
解题方法
5 . 已知三棱锥
中,
与
均为等腰直角三角形,且
,
,
为
上一点,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/3caa1c6d-ee21-41bb-8761-ecd5664213b7.png?resizew=189)
(1)求证:
;
(2)过
作一平面分别交
,
,
于
,
,
,若四边形
为平行四边形,求多面体
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0870247d35bf60ae14239f608da44759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/3caa1c6d-ee21-41bb-8761-ecd5664213b7.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed21f410e8e459d9bd363a739d37336e.png)
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2020-05-22更新
|
1308次组卷
|
5卷引用:2020届湖北省八校(黄冈中学、华师一附中、襄阳四中、襄阳五中、荆州中学等)高三下学期第二次联考数学(文)试题
15-16高三上·上海浦东新·期中
名校
6 . 如图,在四棱柱
中,侧棱
底面
,
,
,
,
,
,
,(
)
平面
;
(2)若直线
与平面
所成角的正弦值为
,求
的值;
(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/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c0ad79161fb29ec231dd0248623ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9740124a284f336f20c98695af04ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5cab760038d20eac10fe6108fbb334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f991c5086ba855802b0331c4e02e3f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223036d27be5914db50fbd5cb19d4212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4e6eb3663870ed202cc208eaf239dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)现将与四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7a84d7e5d6236009a8be655bd500fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7a84d7e5d6236009a8be655bd500fd.png)
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2020-02-05更新
|
846次组卷
|
5卷引用:上海市华东师大二附中2016届高三上学期期中数学试题
(已下线)上海市华东师大二附中2016届高三上学期期中数学试题(已下线)上海市华东师范大学第二附属中学2020-2021学年高二下学期期中数学试题北京市一零一中学2021-2022学年高二上学期期末考试数学试题(已下线)第一章 空间向量与立体几何(压轴必刷30题4种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)辽宁省实验中学2024届高三考前模拟数学试卷
真题
名校
7 . 某个实心零部件的形状是如图所示的几何体,其下部是底面均是正方形,侧面是全等的等腰梯形的四棱台
,上不是一个底面与四棱台的上底面重合,侧面是全等的矩形的四棱柱
.
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570887263182848/1570887268638720/STEM/3dd49ed6521c42be873b7749c33bb2f4.png?resizew=179)
(1) 证明:直线
平面
;
(2)现需要对该零部件表面进行防腐处理,已知
(单位:厘米),每平方厘米的加工处理费为
元,需加工处理费多少元?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0424446817f60c18f8e4e3cc202ad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3a7291238095fcdec7e7ede4ed7274.png)
![](https://img.xkw.com/dksih/QBM/2012/6/15/1570887263182848/1570887268638720/STEM/3dd49ed6521c42be873b7749c33bb2f4.png?resizew=179)
(1) 证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117e9353aec012c49b7517c563bee36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/464afab353a647b4d7addaf021cea2ed.png)
(2)现需要对该零部件表面进行防腐处理,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09cfb3f407089991a1dd9295aa5fb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e991e7f1c5b19446a8e9845d671e48.png)
您最近一年使用:0次
2016-12-01更新
|
1514次组卷
|
2卷引用:2012年全国普通高等学校招生统一考试文科数学(湖北卷)