解题方法
1 . 某三棱锥的三视图如图所示,则此三棱锥外接球的体积是______ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/7fc7a00c-b90e-4263-9c2e-e7ee977d9a62.png?resizew=189)
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解题方法
2 . 如图所示,在长方体中,点
是棱
上的一个动点,若平面
与棱
交于点
,给出下列命题:
①四棱锥的体积恒为定值;
②四边形是平行四边形;
③当截面四边形的周长取得最小值时,满足条件的点
至少有两个;
④直线与直线
交于点
,直线
与直线
交于点
,则
、
、
三点共线.
其中真命题是( )
A.①②③ | B.②③④ | C.①②④ | D.①③④ |
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解题方法
3 . 已知三棱锥
中,
,
,
,
,且平面
平面
,则该三棱锥的外接球的表面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/cb37e547-25d2-4024-9350-e22273b0799c.png?resizew=161)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1abc76f45f1b7e285f2b130d16bf6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a156363bb1b251816b8a5982cc9425a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/cb37e547-25d2-4024-9350-e22273b0799c.png?resizew=161)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知A,B,C为球O的球面上的三个点,
为△ABC的外接圆,若
的面积为12π,
,则当△ABC的面积最大时,球O的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a716a24c456f9b3b765cf25f1cf595d.png)
A.84π | B.96π | C.180π | D.192π |
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解题方法
5 . 某三棱锥的三视图如图所示,则该三棱锥中最长的棱的长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/1c9ec7e0-e994-41e4-9624-92b006828674.png?resizew=156)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/1c9ec7e0-e994-41e4-9624-92b006828674.png?resizew=156)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-23更新
|
655次组卷
|
5卷引用:内蒙古包头市2023届高三二模文科数学试题
内蒙古包头市2023届高三二模文科数学试题内蒙古包头市2023届高三二模理科数学试题内蒙古自治区乌兰察布市2023届高三二模理科数学试题(已下线)专题12立体几何(选填)(已下线)专题12立体几何(选填)
6 . 如图,四棱锥
中,侧面
底面ABCD,
,
,
,
,E,F分别是SC和AB的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/9ddbb321-3b90-4943-9976-dbfd3ebbb5f6.png?resizew=230)
(1)证明:
平面SAD;
(2)点P在棱SA上,当
与底面
所成角为
时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d1553f6806c1eee3b17b94d23f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03766e254c3185d20f5f6d93fa6950d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3165e97ffc02c3d21a79f4e9f34ff368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42bcbc8c13e55d56ca7c483a778e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0cedfb76e95ae3371fad58069554ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/9ddbb321-3b90-4943-9976-dbfd3ebbb5f6.png?resizew=230)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
(2)点P在棱SA上,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abff725851bf24e35a4818af2e85c5c5.png)
您最近一年使用:0次
2023-04-21更新
|
824次组卷
|
3卷引用:内蒙古包头市2023届高三二模理科数学试题
解题方法
7 . 已知A,B,C为球
的球面上的三个点,
为
的外接圆,若
的面积为
,
,则当
的面积最大时,球
的表面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02dba908a505cff93e0b297d00b82a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a716a24c456f9b3b765cf25f1cf595d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2023-04-21更新
|
509次组卷
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4卷引用:内蒙古包头市2023届高三二模理科数学试题
8 . 正多面体共有5种,统称为柏拉图体,它们分别是正四面体、正六面体(即正方体)、正八面体、正十二面体、正二十面体.若连接某正方体的相邻面的中心,就可以得到一个正八面体,已知该正八面体的体积为36,则生成它的正方体的棱长为( )
A.8 | B.6 | C.4 | D.3 |
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2023-04-21更新
|
534次组卷
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5卷引用:内蒙古包头市2023届高三二模文科数学试题
内蒙古包头市2023届高三二模文科数学试题内蒙古包头市2023届高三二模理科数学试题内蒙古自治区乌兰察布市2023届高三二模理科数学试题(已下线)专题12立体几何(选填)(已下线)专题12立体几何(选填)
名校
9 . 如图,四棱锥
的底面
是边长为2的正方形,平面
平面
.平面
平面
,E为
的中点,三棱锥
的体积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/26/298700c5-253f-4ff2-b4e3-4692ef89dd00.png?resizew=183)
(1)证明:
平面
;
(2)求二面角
的正弦值.
![](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/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d492a2248463e0c0199a25d0f76d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/26/298700c5-253f-4ff2-b4e3-4692ef89dd00.png?resizew=183)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0f73cf7ab0c2a8a0099cb2873c81f4.png)
您最近一年使用:0次
2023-03-25更新
|
696次组卷
|
2卷引用:内蒙古赤峰市赤峰二中等校2023届高三下学期二轮复习联考(一)理科数学试题
名校
解题方法
10 . 如图,在正方体
中,
,若
为棱
上动点,
为线段
上的点,且
,若
与平面
所成角的正切值为
,则三棱锥
的外接球表面积为______ .
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc725182c2fd1413319fea35b95c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b7a74708547aec0b942f69ea1192d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f676a67a3dd9284d4d8892b35f23c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa585b9257ed0798213a9ae9b87d291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2965db187e903ddc99b5842adbb2e45e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/16741aed-0bcb-44ec-bbf7-65c35eb3906c.png?resizew=192)
您最近一年使用:0次
2023-03-25更新
|
927次组卷
|
5卷引用:内蒙古赤峰市赤峰二中等校2023届高三下学期二轮复习联考(一)理科数学试题