1 . 唐朝的狩猎景象浮雕银杯如图1所示,其浮雕临摹了国画、漆绘和墓室壁画,体现了古人的智慧与工艺.它的盛酒部分可以近似地看作是半球与圆柱的组合体(假设内壁表面光滑,忽略杯壁厚度),如图2所示.已知球的半径为R,圆柱的高为
.设酒杯上部分(圆柱)的体积为
,下部分(半球)的体积为
,则
的值是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/c8ce4d32-a586-47eb-972a-69f8c23ecfaf.png?resizew=177)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc36cd56e368898b71bc664d30b148e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/c8ce4d32-a586-47eb-972a-69f8c23ecfaf.png?resizew=177)
A.1 | B.2 | C.3 | D.4 |
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2020-07-25更新
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162次组卷
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2卷引用:江苏省淮安市2019-2020学年高一下学期期末数学试题
2 . 如图,设
,
分别是正方体
的棱
上两点,且
,
,其中正确的命题为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/2ecf1b5e-9505-45ca-a166-01606ad85edf.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/2ecf1b5e-9505-45ca-a166-01606ad85edf.png?resizew=171)
A.三棱锥![]() |
B.异面直线![]() ![]() ![]() |
C.![]() ![]() |
D.直线![]() ![]() ![]() |
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2020-05-12更新
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4069次组卷
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15卷引用:江苏省淮安市淮阴中学2019-2020学年高一下学期期末数学试题
江苏省淮安市淮阴中学2019-2020学年高一下学期期末数学试题山东省济南市章丘区第四中学2019-2020学年高二第四次质量检测数学试题(已下线)【新教材精创】1.2.3+直线与平面的夹角(1)B提高练-人教B版高中数学选择性必修第一册江苏省常州市溧阳中学2020-2021学年高三上学期期初考试数学试题山东省青州第一中学东校区2020-2021学年度上学期11月考试高二数学试题(已下线)专题45 空间向量及其应用综合练习-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题08+选择性必修第一册综合练习-2020-2021学年【补习教材·寒假作业】高二数学(人教A版2019)山东省临沂市第四中学2020-2021学年高二年级12月月考数学试题山东省济南市济南第一中学2020-2021学年高二上学期期中数学试题广东省佛山市顺德区郑裕彤中学2019-2020学年高二上学期期中数学试题重庆市育才中学2021-2022学年高二上学期期中数学试题辽宁省辽河油田第一高级中学2021-2022学年高二上学期11月月考数学试题广西玉林市博白县第四中学(博白县中学书香校区)2022-2023学年高二上学期12月段考数学试题河南省尉氏县第三高级中学2023-2024学年高二上学期第一次月考数学试题河南省三门峡市渑池县第二高级中学2023-2024学年高二上学期10月月考数学试题
3 . 若正四棱锥的底面边长为
,侧棱长为
,则该正四棱锥的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
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2019-09-06更新
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1343次组卷
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3卷引用:江苏省淮安市淮阴中学2019-2020学年高一下学期期末数学试题
4 . 一个长方体的三个面的面积分别是
,
,
,则这个长方体的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
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2019-06-07更新
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955次组卷
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3卷引用:江苏省淮安市2018-2019学年度高一年级下学期期末数学试题
5 . 若圆锥的侧面展开图是半径为4的半圆,则此圆锥的体积为______ .
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2019-03-04更新
|
1103次组卷
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7卷引用:【市级联考】江苏省淮安市2018-2019学年高二第一学期期末调研测试数学试题
6 . 如图为一个已搭好的临时帐篷,其形状为五面体ABCDEF,底面四边形ABCD为矩形,
,
是正三角形,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/2019/3/2/2151819811414016/2153075423232000/STEM/d0feab9d-184b-48da-b8ba-69abd261d709.png)
若
,
求五面体ABCDEF的侧面积;
若
,
,问AD长为多少时,五面体ABCDEF的体积最大.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0f194fbe56c418746fdafb35d63d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac11d081a0da527109f6a347ebd561b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa4e62679b78252b9caaa350e84e215.png)
![](https://img.xkw.com/dksih/QBM/2019/3/2/2151819811414016/2153075423232000/STEM/d0feab9d-184b-48da-b8ba-69abd261d709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f7ae09399d99a10c18499fe7990a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62e7d8bf5165e940cfe663e7d5d3f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f367cbfad872a8c8adec534775a6622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbcbb19fceaccc80a799427ec7592119.png)
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7 . 若两个不同圆柱的侧面展开图均是长为4宽为3的矩形,则两圆柱的体积之比为__________ .
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8 . 如图,长方体
中,
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/2012/4/7/1570832315244544/1570832320667648/STEM/e1443962bd84470f94d6115b33a344b7.png?resizew=145)
(1)求证:直线
平面
;
(2)求证:平面
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212f4416ce8fcd69b531ceda6f6ebfbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d7987d716d34f95f439f09317e30b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/2012/4/7/1570832315244544/1570832320667648/STEM/e1443962bd84470f94d6115b33a344b7.png?resizew=145)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be58b9f1bf193fd00d94476cd35b5f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762af1c6ff7d271a0535f94db18e7980.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae1de3f5eb55a078a2dc8d2a585b86a.png)
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12-13高二上·江苏淮安·期末
解题方法
9 . 如图,已知四棱锥
中,底面
是直角梯形,
是线段
上不同于
的任意一点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d5c6539e3a0be85cc27ba7d9b82767.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777558638592/1570777564184576/STEM/4ba308e5b54a49c7a97d17790654c2d5.png?resizew=295)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求三棱锥
的体积.
![](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/9ee4cf5af36d0f1e25d943835b785f70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beeed35864dc79acbe7746c2c8f9118a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaa712e64750e3e2843bae68ebad6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d5c6539e3a0be85cc27ba7d9b82767.png)
![](https://img.xkw.com/dksih/QBM/2012/2/27/1570777558638592/1570777564184576/STEM/4ba308e5b54a49c7a97d17790654c2d5.png?resizew=295)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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