名校
解题方法
1 . 已知直三棱柱
,
,
,
,
,设该直三棱柱的外接球的表面积为
,该直三棱柱内部半径最大的球的表面积为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a39f04d1c3551403dbbed35deb01232.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2021-08-27更新
|
1274次组卷
|
8卷引用:云南省师范大学附属中学2022届高三高考适应性月考卷(二)数学(文)
名校
2 . 已知正方体
的棱长为
,点
是棱
的中点,点
在四边形
内(包括边界)运动,则下列说法正确的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/fa0c60e1-51fb-47b9-a0c5-0bda7bf7fd03.png?resizew=198)
①若
是线段
上,则三棱锥
的体积为定值
②若
在线段
上,则
与
所成角的取值范围为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a52298e06894173520ca36a565bef5.png)
③若
平面
,则点
的轨迹的长度为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
④若
,则
与平面
所成角正切值的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5569c257d122b7837b636d732033531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/fa0c60e1-51fb-47b9-a0c5-0bda7bf7fd03.png?resizew=198)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb438ee6d641962cb80c880f1bf84c1.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a52298e06894173520ca36a565bef5.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e0d886ac00c4a5c0fe764d566ec62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dee6c1410e79934b560642684807e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5569c257d122b7837b636d732033531.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
3 . 已知四棱锥
的底面ABCD是边长为2的正方形,且
.若四棱锥P-ABCD的五个顶点在以4为半径的同一球面上,当PA最长时,则四棱锥P-ABCD的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860c4c9419ebfa927b3f3ea14e4f4784.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
1516次组卷
|
8卷引用:江苏省常州市前黄高级中学2021届高三下学期学情检测(一)数学试题
江苏省常州市前黄高级中学2021届高三下学期学情检测(一)数学试题(已下线)2021年新高考北京数学高考真题变式题6-10题(已下线)专题11 空间几何体-备战2022年高考数学(理)母题题源解密(全国甲卷)(已下线)专题14 空间几何体-备战2022年高考数学(文)母题题源解密(全国甲卷)(已下线)2022年全国高考乙卷数学(文)试题变式题1-4题(已下线)2022年全国高考乙卷数学(理)试题变式题21-23题(已下线)2022年全国高考乙卷数学(理)试题变式题9-12题(已下线)2022年全国高考乙卷数学(文)试题变式题9-12题
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4 . 在平面直角坐标系
中,已知圆
,
是直线
上的两点,若对线段
上任意一点
,圆
上均存在两点
,使得
,则线段
长度的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef47427f5cf639edae3e2523ee0c8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f61de965b9d38982e5a75af2737e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b6a4ad569a245f3238e6713ae8d450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
A.2 | B.![]() | C.![]() | D.4 |
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|
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|
8卷引用:黑龙江省哈尔滨市第三中学2021-2022学年高二上学期10月月考数学(普通班)试题
解题方法
5 . 如图,四边形
中
,
,
,沿直线
将
折成
,使点
在平面
上的射影在
内(不含边界),记二面角
的平面角大小为
,直线
、
与平面
所成角分别为
、
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/0b165d48-127f-4f6f-9fb4-ce1281ce1e06.png?resizew=121)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b88780f9a4bc3110cd801d10c4515b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39776e9158fb382a3de6eb1572bcf02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2df93bd15f25096c510b589aad0dfc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd93fd4788cbe4ae8ea1c783633f127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a21897349d3d7c94419692106887153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/0b165d48-127f-4f6f-9fb4-ce1281ce1e06.png?resizew=121)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
6 . 在三棱锥A-BCD中,平面ABD⊥平面BCD,BD⊥CD,且AB=BD=DA=3,
,则三棱锥A-BCD的外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18120a244d3a1f9c1688bf53eb2ad775.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-08-07更新
|
1859次组卷
|
6卷引用:江苏省徐州市2020-2021学年高一下学期期末数学试题
江苏省徐州市2020-2021学年高一下学期期末数学试题江西省赣州市教育发展联盟2021-2022学年高二上学期第7次联考高二数学(文)试题(已下线)专题21 外接球与内接球相关模型-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)(已下线)第8章 立体几何初步(压轴30题专练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)高一数学下学期期末精选50题(压轴版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)江苏省徐州市2023-2024学年高一下学期第一次质量检测数学试题(1)
名校
解题方法
7 . 如图,在三棱锥
的平面展开图中,四边形
是菱形,
,则三棱锥
外接球的表面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/af7be42e-d2d5-46f2-89c1-e502f0017f37.png?resizew=180)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c42bce098904b241986bb91c65ab33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054faf5a7368b3badd44cb0fd91e03b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/af7be42e-d2d5-46f2-89c1-e502f0017f37.png?resizew=180)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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|
5卷引用:陕西省安康市2020-2021学年高二下学期期末文科数学试题
名校
解题方法
8 . 粽子,古时北方也称“角黍”,是由粽叶包裹糯米、泰米等馅料蒸煮制成的食品,是中国汉族传统节庆食物之一,端午食粽的风俗,千百年来在中国盛行不衰,粽子形状多样,馅料种类繁多,南北方风味各有不同,某四角蛋黄粽可近似看成一个正四面体,蛋黄近似看成一个球体,且每个粽子里仅包裹一个蛋黄,若粽子的棱长为
,则其内可包裹的蛋黄的最大体积约为( )
(参考数据:
)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/c1116815-32ae-4cfa-9473-0d2ae444047e.png?resizew=118)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c91ad3232cbcde8272c78893b828d3.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c3679b73e65e934ea84b8de97441e4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/c1116815-32ae-4cfa-9473-0d2ae444047e.png?resizew=118)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
2428次组卷
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13卷引用:安徽省蚌埠市2020-2021学年高一下学期期末数学试题
安徽省蚌埠市2020-2021学年高一下学期期末数学试题(已下线)第08讲 简单几何体的表面积和体积(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)上海市吴淞中学2021-2022学年高一下学期期末数学试题辽宁省部分中学2021-2022学年高三下学期期末数学试题(已下线)9.6 立体几何与空间向量专项训练安徽省合肥市肥东县综合高中2021-2022学年高一下学期期末考试数学试题(已下线)模块五 倒数第7天 立体几何天津市十二区重点学校2023届高三下学期联考(二)考前模拟数学试题河北省赵县中学2022-2023学年高一下学期5月月考数学试题河北省石家庄市五校联合体2022-2023学年高一下学期期中数学试题(已下线)高一下学期期末真题精选(常考60题29个考点专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)天津市第四十七中学2024届高三上学期第三次阶段性检测数学试题(已下线)模块五 专题四 全真能力模拟2(高一期中模拟)
名校
9 . 如图,
是边长为
的等边三角形,点
在
所在平面外,平面
平面
,点
是棱
的中点,点
分别在棱
上,且
,
. 现给出下列四个结论:①
平面
;②
是定值;③三棱锥
体积的最大值是
;④若三棱锥
的体积是
,则该三棱锥外接球的表面积是
.其中正确结论的个数是( )
![](https://img.xkw.com/dksih/QBM/2021/7/30/2775558110601216/2778914752757760/STEM/98f15ea6-9997-4185-ad37-3150592fd438.png?resizew=285)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d4b113b22890bc910fa4502812f8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bb827adb2c31957a566704ed957c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d14733aa8ee1b11bc861cd581156ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209e3b87346e057276f0692a7361e446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ca820a456491348e72587e4fe10bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8a91062cd1f6e139960b219e9eeb26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2daa8c54f9228940bdcbb91638f3e4cc.png)
![](https://img.xkw.com/dksih/QBM/2021/7/30/2775558110601216/2778914752757760/STEM/98f15ea6-9997-4185-ad37-3150592fd438.png?resizew=285)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
10 . 已知菱形
,
,
为边
上的点(不包括
),将
沿对角线
翻折,在翻折过程中,记直线
与
所成角的最小值为
,最大值为
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb398137779190b35492d9f06d5fbc3.png)
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9卷引用:浙江省丽水市2020-2021学年高二下学期期末数学试题
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