1 . 图,P是圆锥的顶点,
是底面圆O的一条直径,
是一条半径.且
,已知该圆锥的侧面展开图是一个面积为
的半圆面.
(1)求该圆锥的体积;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79684a6e92297749c005e2b23cac9710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4986217611fc5eefe70fd217a9d5726a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/11/023fa059-d0ec-493e-bad2-a485508b98c3.png?resizew=109)
(1)求该圆锥的体积;
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
2020-10-02更新
|
487次组卷
|
2卷引用:湖北省武汉市江岸区2019-2020学年高一下学期期末数学试题
名校
2 . 我国南北朝时期数学家、天文学家——祖暅,提出了著名的祖暅原理:“缘幂势即同,则积不容异也”.“幂”是截面积,“势”是几何体的高,意思是两等高几何体,若在每一等高处的截面积都相等,则两立方体体积相等.已知某不规则几何体与如图三视图所对应的几何体满足“幂势同”,则该不规则几何体的体积为
![](https://img.xkw.com/dksih/QBM/2019/1/20/2122643352322048/2123629380395008/STEM/b2f88786e8e241f58c451762bb45ee23.png?resizew=254)
![](https://img.xkw.com/dksih/QBM/2019/1/20/2122643352322048/2123629380395008/STEM/b2f88786e8e241f58c451762bb45ee23.png?resizew=254)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-01-21更新
|
786次组卷
|
5卷引用:【市级联考】湖北省十堰市2019届高三模拟试题文科数学试题
3 . 如图,四棱锥
中,底面ABCD为矩形,点E在线段PA上,
平面BDE.
求证:
;
若
是等边三角形,
,平面
平面ABCD,四棱锥
的体积为
,求点E到平面PCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0f2891147526d06af8d1ea41c9015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1d28454646730517cec5690e1f8074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9026fbd7897d459b4d559a4b99f2e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6602a9e044cd0719f0380ae97aff6a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebbb79892c8cb8871a08437acc09bc80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e0e8c3310c88ac5b66503f39e07d97.png)
您最近一年使用:0次
2018-12-17更新
|
894次组卷
|
5卷引用:湖北省部分重点中学2020-2021学年高一下学期5月联考数学试题
4 . 如图,
、
分别是三棱锥
的棱
、
的中点,
,
,
,则异面直线
与
所成的角为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/36bbbc3d-7745-4a65-b0ba-725a13cd9c7a.png?resizew=155)
![](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/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c893198d60f9129971aabf596d0ec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec82d5207daadaefea6846b4036347a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/36bbbc3d-7745-4a65-b0ba-725a13cd9c7a.png?resizew=155)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
5 . 已知
、
是球
的球面上的两点,
,点
为该球面上的动点,若三棱锥
体积的最大值为
,则球
的表面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e21aa38de80da8ccaa7ce51595e7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 如图,在四棱锥
中,
底面ABCD,底面ABCD为梯形,
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a92932d5-fbb2-4d32-9c31-393b372e8196.png?resizew=168)
(1)在PD上是否存在一点F,使得
平面PAB,若存在,找出F的位置,若不存在,请说明理由;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0facf189b2a3153beb7b9e077d3b1146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a86542e55ad35b90a5c7afd23e8803.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a92932d5-fbb2-4d32-9c31-393b372e8196.png?resizew=168)
(1)在PD上是否存在一点F,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350d224711c8773a7c5a2b34bf40bedc.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2425afeae790f548529e24c81a40560c.png)
您最近一年使用:0次
2020-03-10更新
|
465次组卷
|
3卷引用:湖北省随州市2019-2020学年高二上学期期末数学试题
名校
7 . 如图,在四棱锥
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/42121f7f-e3fc-44ed-90c5-8c7b1a8950d9.png?resizew=189)
(1)证明:
平面
;
(2)若
,
,
为线段
上一点,且
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d028a62fea771beb2d18f0c1bf856c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca5087d262b2830846cb55fb32fbe5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/42121f7f-e3fc-44ed-90c5-8c7b1a8950d9.png?resizew=189)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98c8e36238ad90378e724466fcb6023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd08b502bf0d11788300e7d6ba2fc66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acaf100147efc6dc6feb362be71a7132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
您最近一年使用:0次
2020-03-25更新
|
462次组卷
|
3卷引用:2020届湖北省宜昌市高三下学期3月线上统一调研测试数学(理)试题
8 . 已知向量
,则下列向量中与
成
的夹角的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb8c4ab37e542eb833cbc5935be0e19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
9 . 某几何体的三视图如图所示,则该几何体的体积是( )
![](https://img.xkw.com/dksih/QBM/2020/5/12/2461034366263296/2461183181651968/STEM/f1e87c8c0a3f4fe397252812b70f62e8.png?resizew=164)
![](https://img.xkw.com/dksih/QBM/2020/5/12/2461034366263296/2461183181651968/STEM/f1e87c8c0a3f4fe397252812b70f62e8.png?resizew=164)
A.6 | B.4 | C.3 | D.2 |
您最近一年使用:0次
2020-05-20更新
|
438次组卷
|
2卷引用:湖北省武汉市2020届高三下学期六月供题(二)文科数学试题
名校
10 . 如图,在三棱锥P-ABC中,平面PAC⊥平面ABC,
和
都是正三角形,
, E、F分别是AC、BC的中点,且PD⊥AB于D.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/0178693f-cfc9-4ea6-b3b5-1d6d1e7d3539.png?resizew=164)
(Ⅰ)证明:直线
⊥平面
;
(Ⅱ)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ab13ef156d034b710d811e09b0be34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/0178693f-cfc9-4ea6-b3b5-1d6d1e7d3539.png?resizew=164)
(Ⅰ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9f783884705e6092fd35fd9222dae1.png)
您最近一年使用:0次
2020-01-20更新
|
451次组卷
|
2卷引用:2020届湖北省荆州中学、宜昌一中等“荆、荆、襄、宜四地七校高三上学期期末考试数学(理)试题