名校
解题方法
1 . 如图,在棱长为4的正方体
中,
为
的中点,经过
,
,
三点的平面记为平面
,点
是侧面
内的动点,且
.
,求证:
;
(2)平面
将正方体
分成两部分,求这两部分的体积之比
(其中
);
(3)当
最小时,求三棱锥
的外接球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7146a372ce6a346fae937622a89d6589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021a0a080f9ce719709a73a46c3459de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e0bdfd5676792840d607096ae0555b.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1daf42c1a89bda5f17ce22e49dda533.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8049311621004b8d0f2637d13010db7.png)
您最近一年使用:0次
2023-07-08更新
|
1343次组卷
|
5卷引用:广东省广州市越秀区2022-2023学年高一下学期期末数学试题
广东省广州市越秀区2022-2023学年高一下学期期末数学试题(已下线)第11章 简单几何体(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)(已下线)高一下学期期末复习解答题压轴题二十四大题型专练(2)-举一反三系列(人教A版2019必修第二册)安徽省安庆市怀宁县新安中学2023-2024学年高一下学期6月月考数学试卷
名校
解题方法
2 . 如图,在四面体
中,
为等边三角形,
为以
为直角顶点的直角三角形,
.
,
,
,
分别是线段
,
,
,
上的动点,且四边形
为平行四边形.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
平面
;
(2)设多面体
的体积为
,多面体
的体积为
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0005e1ef60f6ddc5f9a83e3de1ef3b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929fa05b0d1d2643776e0d09bf3fec44.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/8/a5a3d257-1c29-4d14-91f7-32d8c5d642c1.png?resizew=197)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)设多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997e4fa16abb03b00e7db6924e06a566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbdc69d35ac048be3be891555738e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772448efdb1c5fe0899598dd7328fa2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
您最近一年使用:0次
2023-07-04更新
|
1212次组卷
|
2卷引用:重庆市第八中学校2022-2023学年高一下学期期末数学试题
名校
解题方法
3 . 如图所示,该几何体由一个直三棱柱
和一个四棱锥
组成,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a7ad15b77c2cc409bc24adff155819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f535e16e0474f1660d7d0816ee2318.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/16/b60590fa-533c-4e7e-9389-4347388cc73f.jpg?resizew=113)
A.若![]() ![]() |
B.若平面![]() ![]() ![]() |
C.三棱柱![]() ![]() |
D.当该几何体有外接球时,点![]() ![]() ![]() |
您最近一年使用:0次
2023-06-22更新
|
1275次组卷
|
8卷引用:河北省盐山中学2023届高三模拟数学试题
名校
解题方法
4 . 已知长方体
中,
,过点
且与直线
平行的平面
将长方体分成两部分,且分别与棱
交于点
.现同时将两个球分别放入被平面
分成的两部分几何体内.在平面
变化过程中,这两个球半径之和的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc438d52c5d1cd7f1b6322842a8fdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bc70cf1e4f89142cccea300673acf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc936ca31309f842a5074ff01622c12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
5 . 如图,在正四棱台
中,
,
,
,
为棱
,
的中点,棱
上存在一点
,使得
平面
.
(1)求
;
(2)当正四棱台
的体积最大时,证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439cf259dd6137aa31bb99244a04ddfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](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/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3506f78513da0b4a5c522246e71c76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeef9d70a40b75f5f5c7c1859b4b627.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/12/0b7273f7-569d-4a5a-926b-cd6da93cad40.png?resizew=203)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f276ad76c075f4be32ad326d223cf3.png)
(2)当正四棱台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee6a2c9d3843855bf89516bdd6ad5de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeef9d70a40b75f5f5c7c1859b4b627.png)
您最近一年使用:0次
2023-06-11更新
|
855次组卷
|
3卷引用:2023届河南省创新发展联盟大联考仿真模拟预测数学(文科)试题
名校
解题方法
6 . 已知正四面体
的棱长为3,点
满足
,过点
作平面
平行于
和
,设
分别与该正四面体的棱
,
,
相交于点
,
,
,则四边形
的周长为______ ,四棱锥
的体积的最大值为______ .
![](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/e00450e39b838414c5e8b2c8d6b3f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e226d6a1bb4a1410139e5b810ddb3f.png)
您最近一年使用:0次
2023-06-01更新
|
575次组卷
|
4卷引用:江苏省盐城中学2023届高三三模数学试题
江苏省盐城中学2023届高三三模数学试题(已下线)第七章 立体几何与空间向量 第三节?第一课时直线,平面平行的判定与性质(B素养提升卷)(已下线)第七章 立体几何 专题6 立体几何中的最值问题江西省宜春市宜丰中学2023-2024学年高二下学期6月月考数学试题
名校
7 . 如图,已知圆柱母线长为
,底面圆半径为
,梯形
内接于下底面,
是直径,
//
,
,点
在上底面的射影分别为
,
,
,
,点
分别是线段
,
上的动点,点Q为上底面圆内(含边界)任意一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/31/98aa4952-9475-4ca2-9c91-f97436f7b943.png?resizew=166)
A.若面![]() ![]() ![]() ![]() ![]() |
B.若面![]() ![]() ![]() |
C.![]() |
D.当点Q在上底面圆周上运动时,记直线![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-05-29更新
|
795次组卷
|
3卷引用:山东省淄博市2023届高三三模数学试题
名校
解题方法
8 . 在四面体
中,
,
,
,同时平行于
的平面
分别与棱
交于
四点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b047ab015454b7c5072315274e871b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1f0690d47cac82c8d27e10c8444d57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf7c885153243a3f763c4c8e6268247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d3b50b1249d82c4fdd8e07808addb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
A.![]() | B.![]() |
C.四边形![]() | D.四边形![]() |
您最近一年使用:0次
2023-05-14更新
|
997次组卷
|
3卷引用:福建省厦门市2023届高三毕业班第四次质量检测数学试题
9 . 如图所示,在长方体
中,
,
,点E是棱CD上的一个动点,F是BC的中点,
,给出下列命题,其中真命题的( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/27/1ae16440-ede4-477f-a9fe-a5b6e6031d20.png?resizew=180)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac559a91951383ab73b30de16c534e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/27/1ae16440-ede4-477f-a9fe-a5b6e6031d20.png?resizew=180)
A.当E是CD的中点时,过![]() |
B.当点E是线段CD的中点时,点P在底面ABCD所在平面内,且![]() ![]() |
C.对于每一确定的E,在线段AB上存在唯一的一点H,使得![]() ![]() |
D.过点M做长方体![]() ![]() |
您最近一年使用:0次
解题方法
10 . 球
的内接正四面体
中,
、
分别为
、
上的点,过
作平面
,使得
、
与
平行,且
、
到
的距离分别为2,3,则球
被平面
所截得的圆面的面积是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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