名校
解题方法
1 . 如图,在棱长为
的正方体
中,
,
分别是
,
中点,过
,
,
三点的平面与正方体的下底面
相交于直线
.
的位置,并说明作图依据;
(2)正方体被平面
截成两部分,求较小部分几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)正方体被平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193b5b41994c2a4dfa5bb0bc984061cc.png)
您最近一年使用:0次
2023-10-04更新
|
481次组卷
|
3卷引用:安徽省皖东智校协作联盟2024届高三上学期10月联考数学试题
名校
解题方法
2 . 如图,棱长为
的正方体
,点
分别在棱
上,过点
的截面将正方体分割成两部分.
的平面与正方体表面的交线;(无需证明,保留作图痕迹);
(2)若点
分别为
中点,求过点
的截面将正方体分割的较小部分几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3472985d11e56d62b88cc8c5ac25fd82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3472985d11e56d62b88cc8c5ac25fd82.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3472985d11e56d62b88cc8c5ac25fd82.png)
您最近一年使用:0次
2023-06-21更新
|
603次组卷
|
6卷引用:辽宁省六校2022-2023学年高一下学期6月联考数学试题
辽宁省六校2022-2023学年高一下学期6月联考数学试题辽宁省六校协作体2022-2023学年高一下学期第三次考试(6月)数学试题陕西省西安市铁一中学国际部2023-2024学年高一下学期第三月考数学试题河南省开封市五县联考2023-2024学年高一下学期第二次月考数学试题(已下线)8.3.1棱柱、棱锥、棱台的表面积和体积(分层作业)-【上好课】(已下线)11.1空间几何体-同步精品课堂(人教B版2019必修第四册)
名校
解题方法
3 . 如图,在棱长为
的正方体
中,
,
分别是
,
的中点,过
,
,
三点的平面与正方体的下底面
相交于直线
.
(1)画出直线
的位置,保留作图痕迹,不需要说明理由;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/29/959553f7-f390-4d52-bde9-78f0b031321e.png?resizew=160)
(1)画出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49fa04431a92d131d7b0b903139bd867.png)
您最近一年使用:0次
名校
解题方法
4 . 已知四棱锥
中,底面
为直角梯形,
平面
,
,
,
,
,
为
中点,过
,
,
的平面截四棱锥
所得的截面为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/4/60d03f35-7a27-4a8e-95aa-6ad937654395.png?resizew=185)
(1)若
与棱
交于点
,画出截面
,保留作图痕迹(不用说明理由),并证明
.
(2)求多面体
的体积.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2753753faf2cb9a0003aa8e3945159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80137ee8af4684ce558242d8b3f1459.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/4/60d03f35-7a27-4a8e-95aa-6ad937654395.png?resizew=185)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1ead5e71d659442776937400b19e230.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673d35c60271a1f86876bf4005eee23c.png)
您最近一年使用:0次
2023-05-03更新
|
1104次组卷
|
4卷引用:江西省新余市第一中学2022-2023学年高一下学期第二次月考数学试题
江西省新余市第一中学2022-2023学年高一下学期第二次月考数学试题广西邕衡金卷2023届高三一轮复习诊断性联考数学(文)试题(已下线)高一数学下学期第二次月考01(范围:平面向量,解三角形,复数,立体几何)(已下线)重难点6-2 空间几何体的交线与截面问题(8题型+满分技巧+限时检测)
5 . 如图,正四面体
,
(1)找出依次排列的四个相互平行的平面
,
,
,
,使得
,且其中每相邻两个平面间的距离都相等.请在答卷上作出满足题意的四个平面,并简要说明并证明作图过程;
(2)若满足(1)的平面
,
,
,
中,每相邻两个平面间的距离都为1,求该正四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fbf56b3023539b59f7bcee29acc70.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/21fc98e1-5dbe-46a9-9c60-2bb1802386ea.png?resizew=167)
(1)找出依次排列的四个相互平行的平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9177f43add5ca8480daa636afc5862b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a56eca8dc73a0e8f0c6d3a41bb26bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109c658897735fce605120061c38709d.png)
(2)若满足(1)的平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9177f43add5ca8480daa636afc5862b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a56eca8dc73a0e8f0c6d3a41bb26bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fbf56b3023539b59f7bcee29acc70.png)
您最近一年使用:0次
6 . 如图①,在棱长为2的正方体
木块中,
是
的中点.
将该木块锯开,使截面平行于平面
,在该木块的表面应该怎样画线?请在图①中作图,写出画法,并证明.
(2)求四棱锥
的体积;
![](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/a1c1acd7da8817385417e1dff25bfe25.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f067183ddb143d5a2473ea7ab90ad7ae.png)
您最近一年使用:0次
2023-06-13更新
|
296次组卷
|
3卷引用:江苏省南京市外国语学校2022-2023学年高一下学期5月月考数学试题
江苏省南京市外国语学校2022-2023学年高一下学期5月月考数学试题福建省泉州市晋江市第一中学2022-2023学年高一下学期期中数学试题(已下线)第八章 本章综合--汇总本章方法【第三课】“上好三节课,做好三套题“高中数学素养晋级之路
名校
7 . 如图,已知正方体
的棱长为2,P为正方形底面
内的一动点,则以下结论:
(1)三棱锥
的体积为定值;
(2)若点
为
的中点,满足
平面
的点
的轨迹长度为2;
(3)若
,则
点在正方形底面
内的运动轨迹是线段
;
(4)以点
为球心,
为半径的球面与面
的交线长为
.正确的有______ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e7361ffb6d22b31453f636ef5bf45a.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3123da0313d458c833e82aaa234b9117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c58abd0988129da90c2caf256b37233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(4)以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3765f7d2a69e4ad0707e9283801dcfcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/622f6bb6-6184-4598-9b23-890b4444bc66.png?resizew=169)
您最近一年使用:0次
2023-11-16更新
|
527次组卷
|
2卷引用:上海市向明中学2023-2024学年高二上学期12月质量监控考试数学试卷
解题方法
8 . 如图,若正方体的棱长为2,点P是正方体
的上底面
上的一个动点(含边界),E,F分别是棱BC,
上的中点,有以下结论:
①△PAE在平面
上的投影图形的面积为定值;
②平面AEF截该正方体所得的截面图形是五边形;
③
的最小值是
;
④三棱锥P-AEF体积的最小值为
.
其中正确的是________ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
①△PAE在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
②平面AEF截该正方体所得的截面图形是五边形;
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08204b03bc91a4218d3eff5843002fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01961669cd597f61fa48e9853d678bb8.png)
④三棱锥P-AEF体积的最小值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
其中正确的是
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/15/ec976578-787d-44d8-ac67-b3ca5b810fe0.png?resizew=183)
您最近一年使用:0次
名校
9 . 如图,多面体
中,底面
为正方形,
平面
,且
,G为棱
的中点,H为棱
上的动点,有下列结论:
![](https://img.xkw.com/dksih/QBM/2023/3/4/3187265005854720/3189632691404800/STEM/812260ab23e3487898813c9999c89add.png?resizew=147)
①当H为
的中点时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
平面
;
②三棱锥
的体积为定值;
③三棱锥
的外接球的表面积为
.
其中正确的结论序号为______ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6db4765699190f823a4b79a898d9dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef319a6b6527b65dd91c98a590989a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/2023/3/4/3187265005854720/3189632691404800/STEM/812260ab23e3487898813c9999c89add.png?resizew=147)
①当H为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93240c1473e10c736cc33b65053de761.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199098479c92e87304b91871172d46e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02dba908a505cff93e0b297d00b82a40.png)
其中正确的结论序号为
您最近一年使用:0次
23-24高三上·全国·阶段练习
名校
解题方法
10 . 如图,已知正方体
的棱长为2,E,F分别为AB,BC的中点,则下列说法正确的是________ .(填写所有正确说法的序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/5eb42652-409e-4ff4-ba70-783d263418aa.png?resizew=180)
①平面
截正方体
所得截面图形的周长为
;
②点B到平面
的距离为
;
③平面
将正方体
分割成两部分,较小一部分的体积为
;
④三棱锥
的外接球的表面积为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/5eb42652-409e-4ff4-ba70-783d263418aa.png?resizew=180)
①平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab44d33142e571bf155f367a0224a422.png)
②点B到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e23ab2a5db0d58b522f1e2699bfe60.png)
③平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9717d0d1aa041214f440e171b54465.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2517c94dd8e4bd6e1c19778905f7640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375025f01ec49e6d50e45cce5fee8d88.png)
您最近一年使用:0次