1 . 在长方体
中,
,点
为侧面
内一动点,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
平面
,则
的最小值为__________ ,此时点
到直线
的距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febe773ba9273dc5668bdb3fbe039695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
您最近一年使用:0次
7日内更新
|
241次组卷
|
2卷引用:黑龙江省部分学校2023-2024学年高三第三次模拟数学试题
名校
2 . 已知长方体
的底面ABCD为边长是2的正方形,
,E,F分别为棱AB,
的中点,则过
,E,F的平面截长方体
的表面所得截面的面积为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbe9bf116c671711b4a55a9a7822df1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
2024-06-12更新
|
319次组卷
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4卷引用:东北三省部分学校2024届高三下学期押题考试(二)数学试卷
名校
3 . 若长方体
的底面是边长为2的正方形,高为4,E是
的中点,现给出以下四个命题:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b206efdf8aaef5759c5948de711529.png)
②平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
③三棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
④三棱锥
的外接球的表面积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5f9251b20115e4f9bfc2005ef26f86.png)
则正确命题的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b206efdf8aaef5759c5948de711529.png)
②平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af2cbd18021f373cf7c95a4636c9347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d9afa28d00f88cfa342fb72ee85c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d236e214b4cb2ed4a914166280c6841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5f9251b20115e4f9bfc2005ef26f86.png)
则正确命题的序号是
您最近一年使用:0次
2024-06-12更新
|
166次组卷
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2卷引用:四川省遂宁市射洪中学校2024届高三下学期三模理科数学试题
名校
解题方法
4 . 在直四棱柱
中,所有棱长均为2,
,
为
的中点,点
在四边形
内(包括边界)运动,下列结论中正确的是_____ (填序号)
在线段
上运动时,四面体
的体积为定值
②若
面
,则
的最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
③若
的外心为M,则
为定值2
④若
,则点
的轨迹长度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a46dc0bb5d8fa33583817e530a5d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd91ef047f2591dc1406bc0e39934fe6.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea3bcade880af77158e0dc1a6af2980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be61fee6829cb6e6fe17808c1a8fe197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4996e2ab0b3cdb7d3406e038e5a46c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497ad8ec00e4751a797d755753c8e760.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e077661d6c2faacf4a12f6cfba099f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
您最近一年使用:0次
2024-06-11更新
|
410次组卷
|
2卷引用:四川省射洪市2023-2024学年高三下学期高考模拟测试理科数学试题
2024·全国·模拟预测
解题方法
5 . 已知四棱锥
的底面
是边长为
的正方形,
,
平面
,
为线段
的中点,若空间中存在平面
满足
,
,记平面
与直线
分别交于点
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90271643a96d65b3b092fbbdbd61eea0.png)
______ ,四边形
的面积为______ .
![](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/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967f74b8993c61634ceed95edca05ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3dd3fc7dc95d1af9eafb1ea58dd48a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e049faf8852317b6c046904a39134c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211a44ffb09c7413dac58e9cea70fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90271643a96d65b3b092fbbdbd61eea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a255eabf4d401236e1f1a9f35667ba9.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
6 . 在四棱锥
中,底面
为正方形,平面
都与平面
垂直,
,点
分别为
的中点,且
是线段
上一点(包含端点),给出下列结论:①四边形
为等腰梯形;②不存在点
,使得
平面
;③存在点
,使得
;④
的最小值为
.其中所有正确结论的序号为______ .
![](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/a05792860611772f0525f4acc6b06212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5019d74a9497f861a0f755ea31d010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4762d59261265112fef9ac74d5bb9a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f27e1f707fdd30a58d8a019e6a1440c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497b94185aad68ee732a4435b0189c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea3cebae1762106ecd2a4fd56d07763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae7c0b22a09146fe87955159f70454b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c29c3bfdae2d4fbe8a8deaa572a2e6.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
7 . 如图,在四棱锥
中,底面
是平行四边形,
为线段
的中点,过点
分别作平行于平面
、平面
的平面
、平面
,它们将四棱锥
分成三部分.将这三部分依体积从小到大排列,其体积之比为______ .
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868a98a5d6337c3dd9bca228e3545665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
8 . 在以底面为等腰直角三角形的直三棱柱
中,
为底面三角形斜边
上一点,且
,
,
为线段
上一动点,则平面
截三棱柱所得截面面积的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bfe30380decb4ba3f9a6b0598ed922.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b99e5c5bbcbb90e70cc5bcce9fdcf8bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9ce838d7f2790addb9fc0107229525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa23fa14f624ad8212bda55d321362f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bfe30380decb4ba3f9a6b0598ed922.png)
您最近一年使用:0次
解题方法
9 . 已知四棱锥
的底面
为菱形,其中
,点
在线段
上,若平面
平面
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4dec104fa14f59146ff6aff4e92e537.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c48aa8ffe4295e5b6ea0dfedb04972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448cbac9a1ef3de7538a6b30cdc39582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bd91aceffa44c2d0291a73efcd1027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4dec104fa14f59146ff6aff4e92e537.png)
您最近一年使用:0次
名校
10 . 三棱锥
中,
和
均为边长为2的等边三角形,
分别在棱
上,且
平面
平面
,若
,则平面
与三棱锥
的交线围成的面积最大值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409b28f7cb97726646e79709ad25190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1679c3594dd9e0ef6827c00f0ccee296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351079f0bce7726e1c0c1ef341878f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ccae87c245b5acd88047aa70fbdcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2024-04-18更新
|
1085次组卷
|
4卷引用:山东省部分学校2023-2024学年高三下学期4月金科大联考(二模)数学试题