1 . 在正三棱柱
中,
,点
为棱
的中点,则直线
与平面
夹角的正弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
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名校
解题方法
2 . 设直线
与球
有且只有一个公共点
,从直线
出发的两个半平面
截球
的两个截面圆的半径分别为1和
,二面角
的平面角为
,则球
的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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名校
解题方法
3 . 将一边长为
和
的长方形
沿
折成直二面角
,若
在同一球面上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe454700ca7e4bcb9377a4c1a7557ff.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe454700ca7e4bcb9377a4c1a7557ff.png)
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4 . 如图,
是边长为
的正三角形
的一条中位线,将
沿
翻折至
,当三棱锥
的体积最大时,四棱锥
外接球
的表面积为__________ ;过
靠近点
的三等分点
作球
的截面,则所得截面圆面积的最小值是___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5c166065260b74b70324eb09e4d19d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db2b1c641b93caae9b7a82441e4ba70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.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/1dde8112e8eb968fd042418dd632759e.png)
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5 . 中国古代数学瑰宝《九章算术》中记载了一种称为“羡除”的几何体,该几何体是三个面均为梯形,其他两面为三角形的五面体.现有一羡除
,平面
平面
,
,四边形
,
均为等腰梯形,
,则该几何体
的体积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670896f66ac720530bad6c2168cf33c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5130618afb3ca28fbdb0620e7aa78fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/ceb681f3-2470-4613-b915-0a56ef42bfe9.png?resizew=186)
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解题方法
6 . 如图,正三角形ABC中,D,E分别为边AB,AC的中点,其中
,把
沿着DE翻折至
的位置,得到四棱锥
,则当四棱锥
的体积最大时,四棱锥
外接球的球心到平面
的距离为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34dbf33492e5223df78dea34a24ae015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767a4509580709c12bad736e3a3ef9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767a4509580709c12bad736e3a3ef9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767a4509580709c12bad736e3a3ef9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719103f93166bab4828257608e641a9a.png)
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名校
解题方法
7 . 如图,在多面体
中,已知
,
,
,平面
平面
,四边形
是正方形,则点
到平面
的距离是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657d5471e57b894c3833bb3f43ff38ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a1ce226f636a38dcb980164d69e46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a41e1be0d39b6666edcf4f2d5fe7729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653ddc9c58281c1cc096de7c15ed0749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bc51695e51aa8cd2f97d220c8f5340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bc51695e51aa8cd2f97d220c8f5340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719103f93166bab4828257608e641a9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/20/1d8233f1-01f2-4108-b616-35a0747baee0.png?resizew=164)
您最近一年使用:0次
2023-07-16更新
|
214次组卷
|
2卷引用:江西省丰城拖船中学2023-2024学年高二上学期开学测试数学试题
名校
8 . 如图,三棱锥
中,平面
平面BCD,
是边长为2的等边三角形,
,
.若A,B,C,D四点在某个球面上,则该球体的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532aece6cfd67e2a97977eed978dbf2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcf905f3910d9238a44ef647835b3d1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/c03902f3-ab7a-4d90-bd96-ec522c38bae4.png?resizew=200)
您最近一年使用:0次
2023-07-05更新
|
860次组卷
|
7卷引用:江西省彭泽县第二高级中学2022-2023学年高一下学期7月期末数学试题
名校
解题方法
9 . 如图,三棱柱
的各条棱长均为是2,侧棱
与底面ABC所成的角为60°,侧面
底面ABC,点P在线段
上,且平面
平面
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b3ab67310a3b29c4dc150bbac95ed6.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a55d15bb682bc5ca6fc98beb2c65eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b3ab67310a3b29c4dc150bbac95ed6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/26/f0fa3589-e842-4482-9529-22ca7e8d6880.png?resizew=174)
您最近一年使用:0次
2023-06-20更新
|
730次组卷
|
6卷引用:江西省吉安市第三中学2024届高三上学期开学考试(艺术类)数学试题
解题方法
10 . 在棱长为2的正方体
中,
点为
中点,
点在正方形
内运动(含边界),在点
运动过程中,
点到平面
的最小距离是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/936673a4a40bd0e8d8fe0b2ad6330c7c.png)
您最近一年使用:0次