解题方法
1 . 在空间直角坐标系
中,任何一个平面的方程都能表示成
,其中
,
,且
为该平面的法向量.已知集合
,
,
.
(1)设集合
,记
中所有点构成的图形的面积为
,
中所有点构成的图形的面积为
,求
和
的值;
(2)记集合Q中所有点构成的几何体的体积为
,
中所有点构成的几何体的体积为
,求
和
的值:
(3)记集合T中所有点构成的几何体为W.
①求W的体积
的值;
②求W的相邻(有公共棱)两个面所成二面角的大小,并指出W的面数和棱数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa77ecef36d1f376571db97023d4b81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee28816bd2b5c45de9b3c43ea11fe04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb2a0df4f914f1a8e347188098410c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866ee5fa7a027a6038c7fcc07bb39dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eea6d8b11f53b7c276965d93a5877db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d7d30194744f824ee3eb7820c908a2.png)
(1)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e817c2296f0701d3da67888b9f6101ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ad4daf65e0e620cfb24f1334bb8fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6f9e1352b861710d932d9a9fcda889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)记集合Q中所有点构成的几何体的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4afabfd5b4885311f8d9a4bcf791b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
(3)记集合T中所有点构成的几何体为W.
①求W的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3411c87c90bd10bbadd9201630bf45f4.png)
②求W的相邻(有公共棱)两个面所成二面角的大小,并指出W的面数和棱数.
您最近一年使用:0次
名校
解题方法
2 . 如图,在圆锥
中,若轴截面
是正三角形,C为底面圆周上一点,F为线段
上一点,D(不与S重合)为母线上一点,过D作
垂直底面于E,连接
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/4a784b01-e920-40f1-82dd-3d86a0610067.png?resizew=153)
(1)求证:平面
平面
;
(2)若
为正三角形,且F为
的中点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23354ef3b5664149f9c77564d668885f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cbba955e542f4f53713c208c45cf9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/4a784b01-e920-40f1-82dd-3d86a0610067.png?resizew=153)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1010b502298fdffba6d90265a199ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd1c4e883518a7ac5a7517615e47e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2024-03-07更新
|
792次组卷
|
2卷引用:山东省部分名校2023-2024学年高三下学期2月大联考数学试题
名校
解题方法
3 . 在苏州博物馆有一类典型建筑八角亭,既美观又利于采光,其中一角如图所示,为多面体
,
,
,
,
底面
,四边形
是边长为2的正方形且平行于底面,
,
,
的中点分别为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2407d4b99e51c6a8d33cc32972549f9.png)
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/1b33c98e-854e-4684-9ba8-f1a7ce79dff8.png?resizew=453)
(1)证明:
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)一束光从玻璃窗面
上点
射入恰经过点
(假设此时光经过玻璃为直射),求这束光在玻璃窗
上的入射角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb94145069d895e289f871c9deb403a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542b5bc10c7341c04c22244f3ec16e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03733d1465d041a6d6da32bf91a7cff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f3392a792c219bf3f365281ad9bb70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2407d4b99e51c6a8d33cc32972549f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8930099c42933f19d18446c471738a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/1b33c98e-854e-4684-9ba8-f1a7ce79dff8.png?resizew=453)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c536d18163bd4bc3d7573e206a8d538.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31228c7fd89c98d6235ad993d51d413.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31228c7fd89c98d6235ad993d51d413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(3)一束光从玻璃窗面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31228c7fd89c98d6235ad993d51d413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31228c7fd89c98d6235ad993d51d413.png)
您最近一年使用:0次
2023-03-28更新
|
979次组卷
|
3卷引用:山东省昌乐二中2022-2023学年高三下学期二轮复习模拟(二)数学试题
4 . 如图,
分别是圆台上、下底面的直径,且
,点
是下底面圆周上一点,
,圆台的高为
.
![](https://img.xkw.com/dksih/QBM/2022/5/20/2983383443013632/2985729851711488/STEM/6fb38201888646259f7d2b29e435c99c.png?resizew=189)
(1)证明:不存在点
使平面
平面
;
(2)若
,求二面角
的余泫值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01961669cd597f61fa48e9853d678bb8.png)
![](https://img.xkw.com/dksih/QBM/2022/5/20/2983383443013632/2985729851711488/STEM/6fb38201888646259f7d2b29e435c99c.png?resizew=189)
(1)证明:不存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e82bb469f9387fed54e45efd28bd0e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18a490a22cac27417ddc794f00a1941.png)
您最近一年使用:0次
2022-05-23更新
|
1081次组卷
|
5卷引用:山东省东营市胜利第一中学2022届高三仿真演练试题数学押题卷
山东省东营市胜利第一中学2022届高三仿真演练试题数学押题卷湖北省新高考部分校2022届高三下学期5月质量检测数学试题(已下线)专题08 立体几何解答题常考全归类(精讲精练)-1(已下线)专题19 空间几何解答题(理科)-3陕西师范大学附属中学2023届高三下学期十一模理科数学试题
解题方法
5 . 如图①,在梯形
中,
,
,
,
为
的中点,以
为折痕把
折起,连接
,
,得到如图②的几何体,在图②的几何体中解答下列两个问题.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/5/d8972f98-1533-4a48-adb1-c40183d246cc.png?resizew=335)
(1)证明:
;
(2)请从以下两个条件中选择一个作为已知条件,求二面角
的余弦值.
①四棱锥
的体积为2;
②直线
与
所成角的余弦值为
.
注:如果选择两个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30f6595dd643813b11ad71df61a10dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1aa1e2fb67d9bdb5466c49ea298b28c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/5/d8972f98-1533-4a48-adb1-c40183d246cc.png?resizew=335)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
(2)请从以下两个条件中选择一个作为已知条件,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03a08e6ea74ee085ed9dd4a05af94c2.png)
①四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
注:如果选择两个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2022-04-08更新
|
2356次组卷
|
5卷引用:山东省青岛市2022届三下学期一模数学试题
山东省青岛市2022届三下学期一模数学试题(已下线)临考押题卷01-2022年高考数学临考押题卷(新高考卷)(已下线)专题8-2 立体几何中的角和距离问题(含探索性问题)-22023届北京市高考数学仿真模拟试卷1(已下线)模块四 专题7 高考新题型(劣构题专训)拔高能力练(人教A)