解题方法
1 . 在三棱锥
中,
,若该三棱锥的所有顶点均在球
的表面上,则球
的表面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2bccc2821533d3147f5309eb1104b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在正四棱台
中,
,
.若该四棱台的体积为
,则该四棱台的外接球表面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f8b295ee0c7c60e6fe1dbf054ff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa0d73f30a242947aaf7da525926266.png)
您最近一年使用:0次
名校
3 . 如图,在四面体
中,
和
均是边长为6的等边三角形,
,则四面体
外接球的表面积为_________ ;点E是线段AD的中点,点F在四面体
的外接球上运动,且始终保持EF⊥AC,则点F的轨迹的长度为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e20064b8ad6246d4c307f419da145d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
解题方法
4 . 祖暅原理也称祖氏原理,是我国数学家祖暅提出的一个求体积的著名命题:“幂势既同,则积不容异”,“幂”是截面积,“势”是几何体的高,意思是两个同高的立体,如在等高处截面积相等,则体积相等.由曲线
,
,
围成的图形绕y轴旋转一周所得旋转体的体积为V,则V=__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c465114dc2665d74246240b1d4d26ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63f162c4846a76cadee56ae2f42e37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfb4e91d5c6d50ff816b0240c1a7f02.png)
您最近一年使用:0次
2024-06-11更新
|
252次组卷
|
5卷引用:江西省宜春市樟树中学2024届高三下学期高考数学仿真模拟试卷
2024·全国·模拟预测
名校
5 . 在菱形
中,
,
,将
沿
翻折,使二面角
的余弦值为
,则四面体
的外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d185e7050dcf0d8c3a5532e44c68bf.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/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
6 . 如图,在矩形
中,
,
分别在线段
上,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,将
沿
折起,使
到达
的位置,且平面
平面
.若直线
与平面
所成角的正切值为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b3373b9184f33b33addde0e65ca17b.png)
__________ ,四面体
的外接球的表面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87fc54574f5622060fd377eca07f87b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf33d73483c93f24cc6a1d76ef22ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab6fb62038b9207669ce6f8309fb142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd9311e5295f10061deb2872fe04af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/022d6ec638f715ae16dfde9322c64f70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a668bdc78d077a68254fd33bc392a64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a668bdc78d077a68254fd33bc392a64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb34d99a48c5d1d8f21af99c1b70ea49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b3373b9184f33b33addde0e65ca17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa0fccd22de487c09678f5ab841b6e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/22/aa971d67-6cbd-4856-ba26-6f108a93d820.png?resizew=447)
您最近一年使用:0次
解题方法
7 . 在正四面体
中,M为PA边的中点,过点M作该正四面体外接球的截面,记最大的截面半径为R,最小的截面半径为r,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd05adb62374d8ee90daef4a823650c.png)
_________ ;若记该正四面体和其外接球的体积分别为
和
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa4c480d031dedac6e81872836d04cc.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd05adb62374d8ee90daef4a823650c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa4c480d031dedac6e81872836d04cc.png)
您最近一年使用:0次
2024-03-09更新
|
784次组卷
|
2卷引用:江西省红色十校2024届高三下学期2月联考数学试卷
名校
8 . 如图,该“四角反棱柱”是由两个相互平行且全等的正方形经过旋转、连接而成,其侧面均为等边三角形,已知该“四角反棱柱”的棱长为4,则其外接球的表面积为__________ .
您最近一年使用:0次
9 . 在三棱锥
中,
,
,
,当三棱锥
的体积最大时,直线
与平面
的夹角为______ ,三棱锥的外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2679bb0177f68d4c6e80a9a66bca9348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1371fe98a65d8ebd840c8d98346b6d15.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/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
名校
解题方法
10 . 已知点
在半径为
的球面上,过点
作球的两两垂直的三条弦
若
则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddc2b8eaf6e54fc977888b12ae5ccaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3679af6ed28bf81b65a2d2f791ce68bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45d458ce755deae9c15645993f6db65.png)
您最近一年使用:0次
2024-01-31更新
|
618次组卷
|
3卷引用:江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(二)