1 . 如图,在四棱台
中,
平面
,底面
为平行四边形,
,且
分别为线段
的中点.
.
(2)证明:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd66687a8c0d2d00ba430b040e9f647.png)
平面
.
(3)若
,当
与平面
所成的角最大时,求四棱台
的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e658d7985a600629fdf01517fc55c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac18faf9da6221b788020ac0ddf709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fab0d028634166a93c5d80add98dc27.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd66687a8c0d2d00ba430b040e9f647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faec6f7381dbe8daf15b2969f379e3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
7日内更新
|
657次组卷
|
5卷引用:山东省聊城第一中学等部分学校2023-2024学年高一下学期5月质量监测联合调考数学试题
名校
解题方法
2 . 已知PC是三棱锥
外接球的直径,且
,
,三棱锥
体积的最大值为8,则其外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19f0fcacac715a1200770516d1e4a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2024-06-04更新
|
787次组卷
|
3卷引用:山东省菏泽市第一中学八一路校区2023-2024学年高一下学期第三次月考数学试题
3 . 如图,已知正方体
的棱长为
,点
为
的中点,点
为正方形
内
包含边界
的动点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/12cbd7e7-e585-4129-9770-c01157b86069.png?resizew=164)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/12cbd7e7-e585-4129-9770-c01157b86069.png?resizew=164)
A.满足![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.满足![]() ![]() ![]() |
您最近一年使用:0次
2024-03-29更新
|
970次组卷
|
4卷引用:山东省菏泽第一中学南京路校区2024届高三下学期3月月考数学试题
山东省菏泽第一中学南京路校区2024届高三下学期3月月考数学试题湖南省岳阳市2024届高三下学期教学质量监测(二)数学试题(已下线)专题3 立体几何中的范围、最值问题【讲】(已下线)专题4 立体几何中的动态问题【练】
名校
解题方法
4 . 如图,在边长为2的正方形
中,线段BC的端点B,C分别在边
上滑动,且
.现将
分别沿
折起使点
重合,重合后记为点P,得到三棱锥
.现有以下结论:( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083a4cab8a1938036ef42a7af98a45ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af34f4cc1abe3d8cbe695a8b814d1cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18ab7acf07cd29910932cda5bd75ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7aca4ccd1ee7e65e725de12c746c208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7597689c29b7021fbf0aefc3c2585b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095a7c418bf2a5de5e22edb7d419a79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2aaed1e9ead175f30f7130569d0411.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/dc589c9f-9d71-4750-baa4-99dec68a577b.png?resizew=200)
A. ![]() |
B.当B,C分别为![]() ![]() ![]() |
C.x的取值范围为![]() |
D.三棱锥![]() ![]() |
您最近一年使用:0次
2024-01-07更新
|
636次组卷
|
3卷引用:山东省潍坊市昌乐第一中学2024届高三上学期模拟监测数学试题
山东省潍坊市昌乐第一中学2024届高三上学期模拟监测数学试题广东省广州市华南师大附中2024届高三上学期大湾区数学预测卷(一)(已下线)第二章 立体几何中的计算 专题三 空间体积的计算 微点5 空间图形体积的计算方法【培优版】
名校
5 . 在正方体
中,
,
分别为
的中点,
是
上的动点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/3417f302-5f3e-42c4-acf9-0b8f42eed7b1.png?resizew=156)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00bd0bd954971c2d9c9245763119a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/3417f302-5f3e-42c4-acf9-0b8f42eed7b1.png?resizew=156)
A.![]() ![]() |
B.平面![]() ![]() |
C.三棱锥![]() ![]() |
D.过![]() ![]() ![]() |
您最近一年使用:0次
6 . 如图1,某广场上放置了一些石凳供大家休息,这些石凳是由正方体截去八个一样的正三棱锥得到的,它的所有棱长均相同,数学上我们称之为半正多面体(semiregular solid),亦称为阿基米德多面体,如图2,设
,则平面
与平面
之间的距离是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ee01e28681b584f85c8875f053b77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e3ffa7c33dc5ff17b4cce174b9b2ba.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-18更新
|
654次组卷
|
5卷引用:山东省济宁市第一中学2024届高三上学期12月月考数学试题
山东省济宁市第一中学2024届高三上学期12月月考数学试题广东省佛山市第一中学2024届高三上学期第二次调研数学试题(已下线)重难点6-1 空间角与空间距离的求解(8题型+满分技巧+限时检测)(已下线)高一下学期期中复习选择题压轴题十七大题型专练(2)-举一反三系列(人教A版2019必修第二册)(已下线)广东省佛山市第一中学2024届高三上学期第二次调研数学试题变式题6-10
名校
解题方法
7 . 如图,棱长为2的正方体
中,点
分别是棱
的中点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/42586cdf-1250-4e62-9147-6acfa10d74d6.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed906c3cc40665e9e6aace40cd4b7708.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/42586cdf-1250-4e62-9147-6acfa10d74d6.png?resizew=164)
A.直线![]() |
B.![]() ![]() |
C.过点![]() ![]() |
D.点![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-11-15更新
|
380次组卷
|
2卷引用:山东省菏泽市菏泽三中2024届高三上学期12月月考数学试题
名校
解题方法
8 . 在矩形
中,
,现将
沿对角线
翻折,得到四面体
,记二面角
为
,当
在
内变化时,
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9639896487e6cf18e8fd02d2a7ed2087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158e52f966adb85aada4454c2ba6e5ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
名校
9 . 如图,在四棱台
中,底面
是正方形,
,
,
,
.
(1)求证:直线
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c98d0a336e7b78a3164df8231ab050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90b10ae50e3cf8663038cdeb697168c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a61472439de1ba85cfe33840b775f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295aced98768ce261e00fe6660a427a2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/03e3086b-211f-478a-ae50-c6221513297d.png?resizew=169)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2b198824daf85c88054bda90664231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce12587a7129e4a6ba2837214c6c4cdf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0830c440cb5f1b816d17dcdebdba71a3.png)
您最近一年使用:0次
2023-10-12更新
|
770次组卷
|
3卷引用:山东普高大联考2023-2024学年高二上学期10月联合质量测评数学试题
名校
10 . 如图,平面
平面
,四边形
为矩形,且
为线段
上的动点,
,
,
,
.
为线段
的中点时,
(i)求证:
平面
;
(ii)求直线
与平面
所成角的正弦值;
(2)记直线
与平面
所成角为
,平面
与平面
的夹角为
,是否存在点
使得
?若存在,求出
;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58052cd7d89b0d8556f5a082162dc324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6abed28fd7b66cc392d16edc057d834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
(ii)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2730b513bd3359c3dfe6567e04f5ef9.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2730b513bd3359c3dfe6567e04f5ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2246c0e92e8cc344f636ea8f8f9037e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2730b513bd3359c3dfe6567e04f5ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2273ae1ee99cec9c1304323bc9ebf75f.png)
您最近一年使用:0次
2023-07-07更新
|
1333次组卷
|
11卷引用:山东省青岛市第五十八中学2023-2024学年高一下学期第二次阶段性检测数学试题
山东省青岛市第五十八中学2023-2024学年高一下学期第二次阶段性检测数学试题浙江省台州市2022-2023学年高一下学期期末数学试题江西省彭泽县第二高级中学2022-2023学年高一下学期7月期末数学试题江苏省淮阴中学等四校2023-2024学年高三上学期期初联考数学试题(已下线)10.4 平面与平面间的位置关系(第2课时)(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)第10章 空间直线与平面 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)专题15 立体几何解答题全归类(练习)(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)高一下学期期中复习解答题压轴题十八大题型专练(2)-举一反三系列(人教A版2019必修第二册)(已下线)高一下学期期末数学试卷(提高篇)-举一反三系列(人教A版2019必修第二册)(已下线)重组4 高一期末真题重组卷(浙江卷)B提升卷