名校
解题方法
1 . 在四面体ABCD中,
,AB与CD所在的直线间的距离为3,且AB与CD所成的角为
,则四面体ABCD的体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292d0b9ce587bd5df884a988c22ccba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad1b0a76a887783392268ae203ad22.png)
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名校
2 . 三棱锥
的底面是以AC为底边的等腰直角三角形.且
,各侧棱长均为3,点E为棱PA的中点,则E到平面ABC的距离为______ ;三棱锥
的外接球的表面面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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2023-07-14更新
|
222次组卷
|
2卷引用:河北省武邑中学2022-2023学年高一下学期期末数学试题
3 . 已知
是球O的直径,
,C,D是球面上两点,
,
,
与平面
所成的角为
,则四面体
的体积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf126cfed85fa9b7720ec6f7b0008dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
4 . 在直三棱柱
中,
,
,四棱锥
体积为
,则直三棱柱
的外接球的体积为____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b5572c47e668b91304867b9988c7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0c82028e1259f300facd32775a15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/15/b830fa26-d3db-40b2-810d-f889ed2a3b98.png?resizew=122)
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解题方法
5 . 如图,在正方体
中,与
垂直的面对角线可以是__________ .(写出一条即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/2023/7/10/3278024318754816/3278625438359552/STEM/9f2b5ba87cbd4f8c8843d0b01e25356f.png?resizew=195)
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解题方法
6 .
,
分别是棱长为1的正方体
的棱
的中点,点
在正方体的表面上运动,总有
,则点
的轨迹所围成图形的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92ab2e616111dbe7b501161e75ecaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701a0afc50e0a935f6053639f9c57d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/15/8de81bf5-17eb-4c41-b3e4-ebab72d114b7.png?resizew=158)
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解题方法
7 . 如图,在正方体
中,
,E,M,N,P,Q分别为
,
,
,
,
的中点,O为平面
内的一个动点,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42deb27de4ef5c3199ea4e2fe52f1644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942e71dd31ff025c3cc8f74403ba1378.png)
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2023-07-10更新
|
385次组卷
|
2卷引用:广东省云浮市2022-2023学年高一下学期期末数学试题
解题方法
8 . 如图,在棱长为1的正方体
中,E为棱BC上的动点且不与B重合,F为线段
的中点.给出下列四个命题:
的体积最大值为
;
②
;
③
的面积为定值;
④四棱锥
是正四棱锥.
其中所有正确命题的序号是_________ -.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f4e25111f6f589293cead04fbce3013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7151220769212993f40a51c3ab0c7348.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441dec590b47adc3678a291a3ec89a4a.png)
④四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f62f79e2b6bbb509b60d6ae830b5eb8.png)
其中所有正确命题的序号是
您最近一年使用:0次
2023-07-10更新
|
423次组卷
|
5卷引用:北京市延庆区2021-2022学年高一下学期期末考试数学试题
北京市延庆区2021-2022学年高一下学期期末考试数学试题(已下线)专题强化三 直线、平面的平行和垂直问题-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)北京市通州区2022-2023学年高一下学期期末质量检测数学试题(已下线)专题05 空间几何体的结构特征、表面积及体积3种常考题型归类-《期末真题分类汇编》(北京专用)【北京专用】专题15立体几何与空间向量(第四部分)-高一下学期名校期末好题汇编
解题方法
9 . 在四棱锥
中,底面ABCD为正方形,
为等边三角形,二面角
为
,则异面直线PC与AB所成角的余弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
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10 . 如图,在三棱柱
中,侧棱均与底面垂直,侧棱长为
,
,
,点D是
的中点,F是侧面
(含边界)上的动点,要使
平面
,则线段
的长的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bc7774144c164f7ebaeca54fa657e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431e8bf1a5f9ac9a2ec82c11f31a4afe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456175ea34492f0bc025aaab668fa659.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/a36755d1-a471-4107-81d7-3a147a0faead.png?resizew=140)
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