名校
1 . 如图,三棱锥
中,
为等边三角形,且平面
平面
,
,
,且直线
与平面
所成角为
,
;
(2)求二面角
的余弦值;
(3)求三棱锥
外接球的表面积.
![](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/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa1162d5481e2441fe5bc0d49a576b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2898853a3396f0878af9eac934416d.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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解题方法
2 . 如图,在梯形
中,
,
,且
,
,
,在平面
内过点
作
,以
为轴将四边形
旋转一周.
(2)求旋转体的体积;
(3)求图中所示圆锥
的内切球体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a48fb47f5770d96c4b6b0b4c3efa4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd3a8ef35bd20483fc7a18ab606f0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a03e0d9ec888c1c343853295c40318b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397dfc3db79d0fdbbd7a98ae0a0c963d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求旋转体的体积;
(3)求图中所示圆锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a122e25cf4eb9f03ffe5ec823bfc31.png)
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解题方法
3 . 如图是一个奖杯的三视图.
(2)求奖杯的体积(结果取整数,
取3)
(2)求奖杯的体积(结果取整数,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
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解题方法
4 . 材料1.《数学必修二》第八章8.3节习题8.3设置了如下:
作平行于底面的截面,以该截面为底的面挖去一个圆柱,求剩下几何体的表面积和体积.我们称圆柱为圆锥的内接圆柱.
材料2:如图2,底面直径和高均为
的圆锥有一个底面半径为R,高为H的内接圆柱.根据材料1与材料2完成下列问题.
(1)求R与H的关系式;
(2)求圆柱侧面积的最大值;
(3)当高PO的长为
,直径为
的情况下,底面一只蚂蚁从A点出发绕着圆锥一周回到A点,求蚂蚁爬行的最短距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
材料2:如图2,底面直径和高均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ec556703fc98d32003759064c20b14.png)
(1)求R与H的关系式;
(2)求圆柱侧面积的最大值;
(3)当高PO的长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3045a48f7ffa10be67340cb9c48cfa31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ec556703fc98d32003759064c20b14.png)
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5 . 如图,在直三棱柱
中,
,
,
为
的中点.
平面
.
(2)若以
为直径的球的表面积为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95578eba5dd34ca64b5f228640819cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b531aaca9d037a0d047511eec8f350ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504a36c231b8e80724d01649e7c0944f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95265f94a8eb7f76b5db6875246a091d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee527f97d0bfc89f791b728d80e562d3.png)
您最近一年使用:0次
2024-04-20更新
|
1392次组卷
|
3卷引用:广东省湛江市2024届高三下学期二模考试数学试题
6 . 如图,已知一个组合体由一个圆锥
与一个圆柱
构成(圆锥底面与圆柱上底面重合.平面
为圆柱的轴截面),已知圆锥高为3,圆柱高为5,底面直径为8.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/cc11095d-b313-49b4-8d88-1f56512f107d.png?resizew=135)
(1)求这个组合体的体积
(2)设
为半圆弧
的中点,求
到面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/cc11095d-b313-49b4-8d88-1f56512f107d.png?resizew=135)
(1)求这个组合体的体积
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
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解题方法
7 . 已知圆锥的轴截面面积为
,侧面展开图为半圆.
(1)求其母线长;
(2)在此圆锥内部挖去一个正四棱柱,形成几何体
,其中正四棱柱的底面边长为
,上底面的四个顶点在圆锥侧面上,下底面落在圆锥底面内,求几何体E的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604d037b88148502a5608e0285c76f35.png)
(1)求其母线长;
(2)在此圆锥内部挖去一个正四棱柱,形成几何体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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解题方法
8 . 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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9 . 如图1,在
中,
,
,
为
的中点.如图2,圆
为
的外接圆.
(1)将图1中的
绕着直线
旋转
得到一个几何体;求所得几何体的表面积;
(2)将图2中的阴影部分绕着直线
旋转
得到一个几何体,求所得几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d363f7aac42c7adf8d2ddf05978d3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/8/3e18f3ec-a88c-428a-949e-cb08eb7f4cac.png?resizew=258)
(1)将图1中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe639eab78eafd2d40ea70aa5d3f21d.png)
(2)将图2中的阴影部分绕着直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe639eab78eafd2d40ea70aa5d3f21d.png)
您最近一年使用:0次
2023-08-06更新
|
159次组卷
|
2卷引用:广东省佛山市顺德区镇街学校15校2022-2023学年高一下学期第二次联考数学试题
解题方法
10 . 如图为一个组合体,其底面
为正方形,
平面
,
,且
.
(1)证明:
平面
;
(2)证明:
平面
;
(3)求该组合体的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73f874048f9e48ae35ee95bbf443bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3b89860bcc3e950f1b21575579d8bb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/9/9dc94746-58f1-43de-bf25-97ba64a153a3.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564376a88fa74090de9f7694226a6184.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)求该组合体的表面积.
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