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1 . 若某圆柱体的上部挖掉一个半球,下部挖掉一个圆锥后所得的几何体的三视图中的正(主)视图和侧(左)视图如图1所示,则此几何体的表面积是
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573180774187008/1573180780273664/STEM/475b06c0-a09b-443f-814d-7294c42ff0fc.png)
![](https://img.xkw.com/dksih/QBM/2016/11/25/1573180774187008/1573180780273664/STEM/475b06c0-a09b-443f-814d-7294c42ff0fc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:2017届广西梧州高三上摸底联考理数试卷
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2 . 正四棱锥的顶点都在同一球面上,若该棱锥的高为
,底面边长为
,则该球的体积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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10卷引用:2017届广西南宁市高三上第一次摸底考试文数试卷
2017届广西南宁市高三上第一次摸底考试文数试卷(已下线)“8+4+4”小题强化训练(39)与球有关的问题-2022届高考数学一轮复习(江苏等新高考地区专用)甘肃省天水市第一中学2017-2018学年高一上学期第二次考试数学试题人教A版(2019) 必修第二册 必杀技 第8章 第8.3节综合训练甘肃省天水一中2017-2018学年高一(上)期中数学试题甘肃省兰州市东方中学2020-2021学年第一学期高二年级期中文科考试试题甘肃省兰州市兰州东方中学2020-2021学年高二上学期期中数学理科试题浙江省杭州市学军中学2020-2021学年高一下学期期中数学试题(已下线)【新东方】高中数学20210429—017【2021】【高一下】辽宁省大连市辽宁师范大学附属中学2020-2021学年高一下学期5月月考数学试题
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3 . 若某圆柱体的上部挖掉一个半球,下部挖掉一个圆锥后所得的几何体的三视图中的正(主)视图和侧(左)视图如下图所示,则此几何体的体积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/8/8077bdc9-c389-40c2-8e49-26135fbc6f4e.png?resizew=251)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/8/8077bdc9-c389-40c2-8e49-26135fbc6f4e.png?resizew=251)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:2017届广西南宁市高三上第一次摸底考试文数试卷
4 . 如图,边长为
的等边三角形
的中线
与中位线
交于点
,已知
是
绕
旋转过程中的一个图形,则下列命题中正确的是
![](https://img.xkw.com/dksih/QBM/2016/11/3/1573119743074304/1573119749160960/STEM/510287c8558d40c0af54e3383e21aefb.png)
①
;②
平面
;③三棱锥
的体积有最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2454ac838494a7a444b7f80c88289f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a7d5cf4f2bf91fe0f7a99f2ba358c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/2016/11/3/1573119743074304/1573119749160960/STEM/510287c8558d40c0af54e3383e21aefb.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671ca5fd3878bc1027681f6dd67d8b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6af6b37a320eb2c7a28137ab468c34ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/144060c67b7c6666817d3c41f3caff20.png)
A.① | B.①② | C.①②③ | D.②③ |
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5 . 如图所示,正方体的棱长为1,
,则
与
所成角的度数为
![](https://img.xkw.com/dksih/QBM/2016/11/3/1573119743074304/1573119749136384/STEM/86aea4fa02d3436bbc1e31f7b5b2b6c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5358abf1c5be1a565896239e244add2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://img.xkw.com/dksih/QBM/2016/11/3/1573119743074304/1573119749136384/STEM/f9e55688dca74d9283a0884f55f41da4.png)
![](https://img.xkw.com/dksih/QBM/2016/11/3/1573119743074304/1573119749136384/STEM/86aea4fa02d3436bbc1e31f7b5b2b6c7.png)
A.30° | B.45° | C.60° | D.90° |
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6 . 如图,三棱柱
中,
,
,平面
平面
,
与
相交于点
.
![](https://img.xkw.com/dksih/QBM/2016/11/5/1573127701504000/1573127707844608/STEM/3817bfaaf1124d4095ba2cfe5c314b7c.png)
(1)求证:
;
(2)若
在棱
上,且满足
面
,求三棱锥
的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05912af6afe9d3873e1ab45721a0253e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b723f8b32e35d0ea30b35a083eeb59c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73fcf70859f620a7492e1351327725c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2016/11/5/1573127701504000/1573127707844608/STEM/3817bfaaf1124d4095ba2cfe5c314b7c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7eb25abbc97343485634af711062896.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac3d161848b913e5557617fd4f45f49.png)
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7 . 在三棱锥
中,
为等边三角形,边长为
,
面
,
,则此三棱锥的外接球的表面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd35d0f4870f1a741ed46baa908019c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551e4cd76a93de89ea2750160fe74923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967f74b8993c61634ceed95edca05ffd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 某几何体的三视图如图所示,则该几何体的体积等于__________ .
![](https://img.xkw.com/dksih/QBM/2016/10/26/1573095758815232/1573095764803584/STEM/b42b0a74703e46e3a1f12f47ce90335f.png?resizew=178)
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9 . 在四面体
中,
,
,平面
平面
,
,则四面体
的体积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf832217cee8a4b9acad0531714fb91d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4b6c682d7b0741fb1f12a073394fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfaad4c4467e27421876d8f2a4371d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c90da0cd2708481057fe19acebf2ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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解题方法
10 . 如图所示,一个几何体的主视图和左视图都是边长为4的正方形,中间线段平分正方形,俯视图中有一内切圆,则该几何体的全面积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/31525e81-920f-4e9a-b729-7580d1beccf0.png?resizew=205)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/31525e81-920f-4e9a-b729-7580d1beccf0.png?resizew=205)
A.![]() | B.![]() | C.![]() | D.![]() |
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