名校
1 . 已知点
,
,
是圆锥表面上的点,该圆锥的侧面展开图为以点
为圆心,
为半径的半圆,点
是
的中点,点
是
的中点(如图),则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/12/9/2869016708161536/2870100935761920/STEM/1485892e2d2e4409a9ab03be707d3473.png?resizew=227)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://img.xkw.com/dksih/QBM/2021/12/9/2869016708161536/2870100935761920/STEM/1485892e2d2e4409a9ab03be707d3473.png?resizew=227)
A.圆锥的体积为![]() |
B.直线![]() ![]() |
C.圆锥的内切球半径为![]() |
D.以圆锥底面圆心为球心、半径为2的球被平面![]() ![]() |
您最近一年使用:0次
2021-12-11更新
|
617次组卷
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4卷引用:山东省潍坊市2021-2022学年高二上学期高中学科核心素养测评数学试题
山东省潍坊市2021-2022学年高二上学期高中学科核心素养测评数学试题山东师范大学附属中学2021-2022学年高三学业质量检测数学试题(已下线)热点05 空间几何体表面积与体积的计算-2022年高考数学【热点·重点·难点】专练(全国通用)(已下线)专题08几何体与球切、接的问题(讲)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》
名校
解题方法
2 . 学生小雨欲制作一个有盖的圆柱形容器,满足以下三个条件:①可将八个半径为
的乒乓球分两层放置在里面;②每个乒乓球都和其相邻的四个球相切;③每个乒乓球与该容器的底面(或上盖)及侧面都相切,则该容器的高为________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8aa8efe4821843c00269e1422c38973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
您最近一年使用:0次
2021-11-23更新
|
1404次组卷
|
3卷引用:山东省潍坊市2021-2022学年高三上学期期中数学试题
名校
3 . 如图1,在矩形
与菱形
中,
,
,
,
分别是
,
的中点.现沿
将菱形
折起,连接
,
,构成三棱柱
,如图2所示,若
,记平面
平面
,则( )
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844657931567104/2844713479184384/STEM/66b7b4d75a89494d80b15fba956f4073.png?resizew=158)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844657931567104/2844713479184384/STEM/c3c21240789448b48b396eb70adfd673.png?resizew=158)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0041488020a3e19377b18a70fbf82e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c89f9fb5d1a84be8aee78dca23090d.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/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5089d811caeed93dc3bcc108d122a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5214ffa82aa775edc14bf625edd54cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee618381a1176c3f1504cc059eb2010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23205fa9081ee5fe649093380d61640.png)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844657931567104/2844713479184384/STEM/66b7b4d75a89494d80b15fba956f4073.png?resizew=158)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844657931567104/2844713479184384/STEM/c3c21240789448b48b396eb70adfd673.png?resizew=158)
A.平面![]() ![]() | B.![]() |
C.直线![]() ![]() | D.四面体![]() ![]() |
您最近一年使用:0次
2021-11-05更新
|
1004次组卷
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5卷引用:山东省青岛市青岛第五十八中学2021-2022学年高三上学期期中数学试题
山东省青岛市青岛第五十八中学2021-2022学年高三上学期期中数学试题山东省青岛市青岛第十九中学2021-2022学年高三上学期期中数学试题2022年全国著名重点中学领航高考冲刺试卷(一)数学试题(已下线)考点33 直线与平面所成的角【理】-备战2022年高考数学典型试题解读与变式(已下线)热点06 空间位置关系的判断与证明-2022年高考数学【热点·重点·难点】专练(全国通用)
解题方法
4 . 如图,已知正方体
的棱长为2,则下列结论错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/e2f8a3b4-ad51-4dae-9f66-afccb69e76b7.png?resizew=132)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/e2f8a3b4-ad51-4dae-9f66-afccb69e76b7.png?resizew=132)
A.直线![]() ![]() |
B.直线![]() ![]() |
C.将形状为正方体![]() ![]() |
D.若矩形![]() ![]() ![]() ![]() |
您最近一年使用:0次
2021-10-06更新
|
1366次组卷
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6卷引用:山东省济宁市邹城市2020-2021学年高一下学期期中数学试题
山东省济宁市邹城市2020-2021学年高一下学期期中数学试题(已下线)8.4空间点、直线、平面之间的位置关系B卷(已下线)易错点10 立体几何-备战2022年高考数学考试易错题(新高考专用)(已下线)13.3空间图形的表面积和体积-2021-2022学年高一数学10分钟课前预习练(苏教版2019必修第二册)河北省石家庄市元氏县第四中学2021-2022学年高一下学期期末数学试题河北省石家庄市元氏县第四中学2021-2022学年高一下学期期中数学试题
名校
解题方法
5 . 球面几何是几何学的一个重要分支,在航海、航空、卫星定位等方面都有广泛的应用.球面几何中,球面两点之间最短的距离为经过这两点的大圆的劣弧长,称为测地线.已知正三棱锥
,侧棱长为
,底面边长为
,设球
为其外接球,则球
对应的球面上经过
,
两点的测地线长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-08-05更新
|
357次组卷
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4卷引用:山东省威海市2020-2021学年高一下学期期末数学试题
山东省威海市2020-2021学年高一下学期期末数学试题山东省济南外国语学校2021-2022学年高二上学期开学数学试题重庆市缙云教育联盟2021-2022学年高二上学期12月月考数学试题(已下线)模块四 专题2 期末重组综合练(山东)(人教B)
名校
解题方法
6 . 某同学在劳动实践课上制作了一个如图所示的容器,其上半部分是一个正四棱锥,下半部分是一个长方体,已知正四棱锥
的高是长方体
高的
,且底面正方形
的边长为4,
.
的长及该长方体的外接球的体积;
(2)求正四棱锥的斜高和体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
(2)求正四棱锥的斜高和体积.
您最近一年使用:0次
2021-07-11更新
|
565次组卷
|
5卷引用:山东省潍坊市2020-2021学年高一下学期期末数学试题
7 . 在一次综合实践活动中,某手工制作小组利用硬纸板做了一个如图所示的几何模型,底面
为边长是4的正方形,半圆面
底面
.经研究发现,当点
在半圆弧
上(不含
,
点)运动时,三棱锥
的外接球始终保持不变,则该外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3e2bed5ce5fe466395d2f5743d335b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
![](https://img.xkw.com/dksih/QBM/2021/5/25/2728608680091648/2730549494046720/STEM/f0e24e3d-00e2-4183-818e-28b2c1f4da86.png?resizew=271)
您最近一年使用:0次
名校
8 . 某校学生去工厂进行劳动实践,加工制作某种零件.如图,将边长为
cm正方形铁皮剪掉阴影部分四个全等的等腰三角形,然后将
,
,
,
分别沿
,
,
,
翻折,使得
,
,
,
重合并记为点
,制成正四棱锥
形状的零件.当该四棱锥体积最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
___________
;此时该四棱锥外接球的表面积![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
___________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fdaf9c9ae3eb3d4077ea8aa38dd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4163917addcf97a13ba2a601c4c6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dccea04833649f100f410b1c4fbb93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b42d15b184904764e9a374554fc589c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea01783a103b781077cc9534b46efa01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
![](https://img.xkw.com/dksih/QBM/2021/5/6/2715469800931328/2716721934950400/STEM/de740c58-4f2b-486c-a9e9-11e35ad963d2.png?resizew=241)
您最近一年使用:0次
2021-05-08更新
|
745次组卷
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4卷引用:山东省青岛市2021届高三二模数学试题