名校
1 . 如图,在四棱柱
中,底面
和侧面
均是边长为2的正方形.
.
(2)若
,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/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d56889f2417c8449b7ed31a03550d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcb99b46d35b58383fb46737b99e8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee7e8d13fcdce579695d45a366eb7a3.png)
您最近一年使用:0次
2024-02-27更新
|
604次组卷
|
5卷引用:四川省雅安市雅安中学等校联考2024届高三下学期开学考试数学(理)试题
四川省雅安市雅安中学等校联考2024届高三下学期开学考试数学(理)试题山东省济南第一中学等校2024届高三下学期阶段性检测(开学考试)数学试题(已下线)8.6.2平面与平面垂直(已下线)专题3.8 立体中的夹角和距离问题-重难点突破及混淆易错规避(人教A版2019必修第二册)(已下线)重难点专题14 利用传统方法解决二面角问题-【帮课堂】(苏教版2019必修第二册)
2 . 在棱长为
的正方体
中,棱
,
的中点分别为
,
,点
在平面
内,作
平面
,垂足为
.当点
在
内(包含边界)运动时,点
的轨迹所组成的图形的面积等于_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd348158643b586b97e3e6d1f70f5c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/2021/1/31/2647936051642368/2649264842481664/STEM/03d92be0-67ea-403a-8260-8757a5d554e8.png)
您最近一年使用:0次
2021-02-02更新
|
1334次组卷
|
7卷引用:四川省成都市武侯区第七中学2020-2021学年下学期高三数学(理)开学考试试题
四川省成都市武侯区第七中学2020-2021学年下学期高三数学(理)开学考试试题浙江省杭州市2020-2021学年高三上学期期末数学试题浙江省杭州市2020-2021学年高三上学期期末教学质量检测数学试题(已下线)【新东方】高中数学20210304-009(已下线) 专题18 几何体的表面积与体积的求解 (练)-2021年高三数学二轮复习讲练测(新高考版)(已下线) 专题22 几何体的表面积与体积的求解 (练)2021年高三数学二轮复习讲练测-(文理通用)(已下线)专题2 立体几何与解析几何
名校
解题方法
3 . 如图,在四棱锥
中,底面
为矩形,平面
⊥平面
,
,
为
的中点,点
在棱
上.
(1)若
,求三棱锥
的体积;
(2)在线段
上是否存在点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
?若存在,求
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6893df72c3557bc70bf9ae265814da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/10/c355cf93-0422-48c6-8d6e-131e00db8358.png?resizew=229)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb8073dd57b847af2a6685bf92a0c26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075cf637ce0e87579cae42062e95a9c6.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d26526abf0ab6b7c402ea8c7df3744.png)
您最近一年使用:0次
4 . 如图,已知圆
的直径
长为 2 ,上半圆圆弧上有一点
,点
是劣弧
上的动点,点
是下半圆弧上的动点,现以
为折线,将上、下半圆所在的平面折成直二面角,连接
则三棱锥
的最大体积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76742b51590b09ac5b3083c3f04262c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f38a765027a32ad93c4391c842658f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76742b51590b09ac5b3083c3f04262c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02a85ddbb7ce8d115ff7e4412dedea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d352cc181bd3e1172014eadc9ab0e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/1ac91a95-a0b6-4ea6-8a82-3d382a269d29.png?resizew=329)
您最近一年使用:0次
2022-09-12更新
|
331次组卷
|
4卷引用:四川省绵阳市盐亭中学2022-2023学年高二上学期入学考试数学试题
四川省绵阳市盐亭中学2022-2023学年高二上学期入学考试数学试题四川省宜宾市2020-2021学年高一下学期期末数学试题(已下线)第03讲 直线、平面平行垂直的判定与性质(练)(已下线)考向30 立体几何中的最值、翻折、探索性问题(重点)
5 . 如图,四棱柱
中,面
面
,面
面
,点
、
、
分别是棱
、
、
的中点.
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763172884103168/2764333764706304/STEM/24cf440c-ed80-4cd9-8f6d-403eec6550fe.png?resizew=241)
(1)证明:
面
.
(2)若四边形
是边长为
的正方形,且
,面
面
直线
,求直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd14966183389b10618cbe33fd777407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763172884103168/2764333764706304/STEM/24cf440c-ed80-4cd9-8f6d-403eec6550fe.png?resizew=241)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e0aa7d7faf508bacfd7fa5ae00affb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b957201c0a5bbd5902e5f8e4b22d426d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aecd1f2013b1f9df3feb3574d3b5c34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
您最近一年使用:0次
2021-07-14更新
|
494次组卷
|
3卷引用:四川省泸州市泸县第五中学2021-2022学年高二下学期开学考试数学(理)试题
解题方法
6 . 在三棱锥
中,
和
是边长为2的正三角形,且平面
平面
,
是棱
上一点,点
是三棱锥
外接球上一动点,当
的周长最小时,
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1978b59fd41a7e45b66355645142aa4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
您最近一年使用:0次
7 . 已知α,β,γ为平面,
是直线,若α∩β=
,则“α⊥γ,β⊥γ”是“
⊥γ”的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2019-04-10更新
|
620次组卷
|
3卷引用:四川省宜宾市叙州区第一中学校2020-2021学年高三上学期开学考试数学(文)试题
8 . 如图,几何体EF-ABCD中,四边形CDEF是正方形,四边形ABCD为直角梯形,AB∥CD,AD⊥DC,△ACB是腰长为2
的等腰直角三角形,平面CDEF⊥平面ABCD.
(1)求证:BC⊥AF;
(2)求几何体EF-ABCD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
(1)求证:BC⊥AF;
(2)求几何体EF-ABCD的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/011f6c09-0467-41c5-8ac5-536878a529c8.png?resizew=162)
您最近一年使用:0次
2019-01-17更新
|
578次组卷
|
2卷引用:四川省棠湖中学2019-2020学年高二上学期开学考试数学(文)试题
名校
9 . 已知四棱锥
中,平面
平面
,其中
为正方形,
为等腰直角三角形,
,则四棱锥
外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.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/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2019-09-29更新
|
441次组卷
|
2卷引用:四川省双流中学2019-2020学年高二上学期入学考试数学(文)试题
名校
10 . 在
中,已知
,
,
,D是边AC上一点,将
沿BD折起,得到三棱锥
.若该三棱锥的顶点A在底面BCD的射影M在线段BC上,设
,则x的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff008bf9d674fee28e3b4514d0b1c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd96237afe271ec4023459aba08c1304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f2a9b923a355694ea487f6c5669a04.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次