如图,几何体
为一个圆柱和圆锥的组合体,圆锥的底面和圆柱的一个底面重合,圆锥的顶点为P,圆柱的上、下底面的圆心分别为
、
,且该几何体有半径为1的外接球(即圆锥的顶点与底面圆周在球面上,且圆柱的底面圆周也在球面上),外接球球心为O.
,求几何体
的体积;
(2)若
,求几何体
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385f4234cc4bcddd32d5f41aad17257f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
21-22高二上·上海黄浦·期中 查看更多[11]
上海市格致中学2021-2022学年高二上学期期中数学试题山西现代双语学校2021-2022学年高一下学期5月段考数学试题(已下线)重难点02 几何体的表面积、体积、轴截面、多面体与球体内切外接问题 (重难点突破解题技巧与方法)-2022-2023学年高二数学考试满分全攻略上海市第二中学2021-2022学年高二上学期12月月考数学试题(已下线)专题8.18 立体几何初步全章综合测试卷(提高篇)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)第07讲 空间几何体初步-【寒假预科讲义】(人教A版2019必修第一册)(已下线)第11章 简单几何体(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)(已下线)高一下学期期中数学试卷(提高篇)-举一反三系列(已下线)专题8.11 立体几何初步全章十四大压轴题型归纳(拔尖篇)-举一反三系列(已下线)专题15 简单几何体的表面积与体积-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)第八章 本章综合--提炼本章思想【第二课】“上好三节课,做好三套题“高中数学素养晋级之路
更新时间:2021-11-22 21:07:38
|
相似题推荐
解答题-证明题
|
较难
(0.4)
名校
【推荐1】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
【推荐2】如图所示,用一个不平行于圆柱底面的平面,截该圆柱所得的截面为椭圆面,得到的几何体称之为“斜截圆柱”.图一与图二是完全相同的“斜截圆柱”,AB是底面圆
的直径,
,椭圆所在平面垂直于平面ABCD,且与底面所成二面角为
,图一中,点
是椭圆上的动点,点
在底面上的投影为点
,图二中,椭圆上的点
在底面上的投影分别为
,且
均在直径AB的同一侧.
时,求
的长度;
(2)(i)当
时,若图二中,点
将半圆均分成7等份,求
;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526908dfb46cf151b8ab1492a9d52047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1d663b6001346d11600f064cfcb7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d26ebb800066a7bce57213cd074005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d26ebb800066a7bce57213cd074005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b20bf4f818b494e7b5fa9c68527026e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893ff0f9b64c66312c37cb7ce90c351d.png)
(2)(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bde134aa77da12366e6a742fa33b4bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e578d74f75cf5a087cb5dbad1d07c66.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0838e80d58bad3e9cbc4766d2a0ec3.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
解题方法
【推荐1】某艺术品公司欲生产一款迎新春工艺礼品,该礼品是由玻璃球面和该球的内接圆锥组成,圆锥的侧面用于艺术装饰,如图1.为了便于设计,可将该礼品看成是由圆
及其内接等腰三角形
绕底边
上的高所在直线
旋转
而成,如图2.已知圆
的半径为10cm,设
,
圆锥的侧面积为
cm2.
![](https://img.xkw.com/dksih/QBM/2020/9/3/2542001033773056/2544152920940544/STEM/32866095c84a40b1ba0072d2620d301d.png?resizew=151)
![](https://img.xkw.com/dksih/QBM/2020/9/3/2542001033773056/2544152920940544/STEM/8df1f56dbf404d32a981bcbd2fb7216e.png?resizew=151)
![](https://img.xkw.com/dksih/QBM/2020/9/3/2542001033773056/2544152920940544/STEM/b79476508b0c402e8b8608f91a729684.png?resizew=151)
(1)求
关于
的函数关系式;
(2)为了达到最佳观赏效果,要求
最大,求
的最大值并求此时腰
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe639eab78eafd2d40ea70aa5d3f21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588688304039065c026f2e12bd81b680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45c89d1cb5a4f758539bdda2e31fa94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://img.xkw.com/dksih/QBM/2020/9/3/2542001033773056/2544152920940544/STEM/32866095c84a40b1ba0072d2620d301d.png?resizew=151)
![](https://img.xkw.com/dksih/QBM/2020/9/3/2542001033773056/2544152920940544/STEM/8df1f56dbf404d32a981bcbd2fb7216e.png?resizew=151)
![](https://img.xkw.com/dksih/QBM/2020/9/3/2542001033773056/2544152920940544/STEM/b79476508b0c402e8b8608f91a729684.png?resizew=151)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)为了达到最佳观赏效果,要求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6027609dfc0862ba9077900d39acebca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
【推荐2】如图,在正六棱锥
中,球
是其内切球,
,点
是底面
内一动点(含边界),且
.
的体积;
(2)当点
在底面
内运动时,求线段
所形成的曲面与底面
所围成的几何体的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b7838a53d0b3ed4565fb6a890f365d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b8cac7e05ce1f496a81d8903913bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a187f0d36def464baefc8919ce24c20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b7838a53d0b3ed4565fb6a890f365d.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
解题方法
【推荐1】如图,四边形ABCD是圆柱底面的内接四边形,是圆柱的底面直径,
是圆柱的母线,E是AC与BD的交点,
,
.
(1)记圆柱的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
(2)设点F在线段AP上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0724089d732523d6f5d0f0fbc6f64984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5744f53b3376ffbe7a6bc5044c861273.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐2】如图,已知三棱柱
的侧棱垂直于底面,
,
,点
,
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/23400cdf-6e8e-4b56-aeaf-5954342cf0fe.png?resizew=158)
(1)若
,求三棱柱
的体积;
(2)证明:
平面
;
(3)请问当
为何值时,
平面
,试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8684078379a9e6b209068e1de693af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9806df6df27bf715c81c4a93fc6517c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f3cbee923ebf5179770f7dbb53b38f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/23400cdf-6e8e-4b56-aeaf-5954342cf0fe.png?resizew=158)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c15dd981c5b6dbfd5b3f6462a624b83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8684078379a9e6b209068e1de693af0.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63515a3fe55a14fa7f87dfc1ed9626ee.png)
(3)请问当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e416ca9e681b92c492cfedfa19b05e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c25c4259d935d6e6fabe5c3fc1f43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd97452bd150c579f4fb571a85e12cfa.png)
您最近一年使用:0次