名校
解题方法
1 . 已知一个三棱锥的三视图如图所示,正视图为正方形,侧视图和俯视图均为直角三角形,则该几何体的体积是( )
![](https://img.xkw.com/dksih/QBM/2022/4/6/2952476810829824/2952971693842432/STEM/4072fafb-a356-445e-9ded-ee9090f5c3e8.png?resizew=166)
![](https://img.xkw.com/dksih/QBM/2022/4/6/2952476810829824/2952971693842432/STEM/4072fafb-a356-445e-9ded-ee9090f5c3e8.png?resizew=166)
A.12 | B.2 | C.4 | D.6 |
您最近一年使用:0次
2022-04-07更新
|
712次组卷
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4卷引用:云南师范大学附属中学2022届高三高考适应性月考卷(九)数学(理)试题
名校
2 . 如图所示,直三棱柱
的所有棱长均相等,点D为
的中点,点E为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/30/2947492456726528/2948197200707584/STEM/9b5f946b-1299-44bd-ab8a-b2216485d728.png?resizew=139)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
平面
;
(2)若三棱锥
的体积为
,求该三棱柱的外接球表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/2022/3/30/2947492456726528/2948197200707584/STEM/9b5f946b-1299-44bd-ab8a-b2216485d728.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c2bd5eaf71f8866c0979fa299df50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a8b76e36783a69d14ec54af82c7df0.png)
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解题方法
3 . 如图1,在
中,
,点
,D是
的三等分点,点
,C是
的三等分点,分别沿
和DC将
和
翻折,使平面
平面ABCD,且
平面ABCD,得到几何体
,作
于E,连接AE,
,
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9c76e352-ef99-4431-9494-17c66f534bf9.png?resizew=345)
(1)证明:图2中,
;
(2)若
,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343dddd8341503ede1249d94d93090d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67342548c790676a7f59eaafa89e2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee50e904fed4ad9c6292bec0b08a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab01dbac75a51c89c9d44395cd649985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf1d7f75c7da29c8b189c5ccb4e7a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000a5d60075d7f1b9471cb12c18ebecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52eab6de89f4d4e69650e94e0968744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1992c4aaf4b709b7be1d0de58c2e119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9c76e352-ef99-4431-9494-17c66f534bf9.png?resizew=345)
(1)证明:图2中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67baffab4177197abf8668569aad656.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9666b03b544efac31b8f8ed7ddb7a427.png)
您最近一年使用:0次
4 . 如图,一块边长为4cm的正方形纸片上有四块阴影部分,将这些阴影部分裁下来,然后用余下的四个全等的等腰三角形和一个正方形做成一个正四棱锥,则该正四棱锥的体积为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d1d99afa158b4ba4fc0dae562fcc1.png)
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946076082823168/2947635907051520/STEM/dc80d0e6f39f4265afdc391311f24b39.png?resizew=192)
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2022-03-30更新
|
802次组卷
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4卷引用:云南省昆明市2022届高三”三诊一模“复习教学质量检测数学(文)试题
5 . 已知A,B,C是表面积为
的球O的球面上的三个点,且
,
,则三棱锥
的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95345846d2dd4dfa042a9093c62a8b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2f042901f9931fcc9b418752261d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb01d2b57580731c8b807ac8cffc8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-03-22更新
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4349次组卷
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15卷引用:云南省2022届高三“3+3+3”高考备考诊断性联考(二)数学(理)试题
云南省2022届高三“3+3+3”高考备考诊断性联考(二)数学(理)试题云南省2022届高三“3+3+3”高考备考诊断性联考(二)数学(文)试题云南省大理州鹤庆县第三中学2023届高三上学期第二次月考数学试题西南名校联盟2022届“3+3+3”高考备考诊断性联考卷(二)文科数学试题西南名校联盟2022届“3+3+3”高考备考诊断性联考卷(二)理科数学试题陕西省渭南市2022届高三下学期二模文科数学试题广西桂林、河池、来宾、北海、崇左市2022届高三5月高考联合模拟考试数学(理)试题(已下线)查补易混易错点06 立体几何-【查漏补缺】2022年高考数学(理)三轮冲刺过关湖北省黄冈中学2022届高三下学期二模数学试题河北省衡水中学2022届高考一模数学试题山东省莱西市第一中学2021-2022学年高一下学期华商班6月月考数学试题湖北省黄冈市重点中学2022届高三下学期5月二模数学试题四川省宜宾市叙州区第一中学2022-2023学年高二上学期期末模拟数学(理)试题湖南省益阳市南县立达中学2022-2023学年高一下学期期中数学试题(已下线)8.3.2 圆柱、圆锥、圆台、球的表面积和体积(1)-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)
名校
解题方法
6 . 如图,点
在正方体
的面对角线
上运动(
点异于
点),则下列四个结论:①三棱锥
的体积不变;②
平面
;③
;④平面
平面
.其中说法正确的序号有_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffae5dd516ba282003e4ad9ca1b6fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad99ef5e70de37345c708b758d545f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74827ace228023ae8bdf649a4517c3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d738aec61fee6269dbf8fc9fbd09c276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb955df71b56b325021d2552303285f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/48e5b64c-7d50-4e51-839d-1d33e4ed6bc9.png?resizew=175)
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2022-03-17更新
|
502次组卷
|
4卷引用:云南省昆明市第一中学西山学校2022届高三3月月考数学(理)试题
名校
解题方法
7 . 如图,直四棱柱
的底面是菱形,E,F分别是
上的点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/5ca20417-0a32-4c06-9d65-8e903ddabc6d.png?resizew=160)
(1)证明:点F在平面
内;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ae1236ba2dca7bc34a87533a22e90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23bce37d28bda566bffbc0b7506160d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/5ca20417-0a32-4c06-9d65-8e903ddabc6d.png?resizew=160)
(1)证明:点F在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c47d03028c31e772cc4720c41248e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aca184f73f1bc6fb5191566728a51a8.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在直三棱柱
中,
分别是
的中点,F是棱
上的点,满足
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896532210073600/2926872497266688/STEM/2511dcfd-a9da-46a0-965d-a44046353f48.png?resizew=128)
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ee8a1224b865c6ebc8d68421179ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4b683d829f71b8c5c4b16cb9f7710a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21204d1c00149a21f59c004f6b927237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896532210073600/2926872497266688/STEM/2511dcfd-a9da-46a0-965d-a44046353f48.png?resizew=128)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98dbbf1a30ea54a46b903a9645debab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8964550c7fc31d982b1534e884ad6f52.png)
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2022-03-01更新
|
607次组卷
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3卷引用:云南省师范大学附属中学2022届高三高考适应性月考卷(七)数学(文)试题
9 . 如图,正方体
的棱长为1,
分别为
上的动点,且
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/015d5513-0d41-4c61-9fef-8fa70f5501de.png?resizew=172)
![](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/3da3315c6d0da6a092188a8de1823584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276ff5d6630c81667576db93c882fe42.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/015d5513-0d41-4c61-9fef-8fa70f5501de.png?resizew=172)
A.直线![]() ![]() | B.二面角![]() |
C.直线![]() ![]() ![]() | D.三棱锥![]() |
您最近一年使用:0次
10 . 甲烷是一种有机化合物,分子式为
,其在自然界中分布很广,是天然气、沼气的主要成分.如图所示的为甲烷的分子结构模型,已知任意两个氢原子之间的距离
(H-H键长)相等,碳原子到四个氢原子的距离
(C-H键长)均相等,任意两个H-C-H键之间的夹角为(键角)均相等,且它的余弦值为
,即
,若
,则以这四个氢原子为顶点的四面体的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff19349a80467d65564cc2953f0c978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65abdf27c9e28f330c977d85e77e39a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae6e8f1b46d8d3c95aa0aac54bd4f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e8ad0e1c28c5412964c97cd8ef5ee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d2ee923a118700a40edfcc7f966624.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-01-27更新
|
699次组卷
|
10卷引用:云南省楚雄州2022届高三上学期期末教育学业质量监测数学(文)试题
云南省楚雄州2022届高三上学期期末教育学业质量监测数学(文)试题云南省楚雄州2022届高三上学期期末教育学业质量监测数学(理)试题云南省楚雄彝族自治州牟定县第一高级中学2022届高三上学期期末数学(文)试题云南省楚雄彝族自治州牟定县第一高级中学2022届高三上学期期末数学(理)试题湖北省十堰市2021-2022学年高三上学期元月期末数学试题福建省莆田市2022届高三第一次教学质量检测数学试题(已下线)技巧01 选择题解法与技巧(讲)--第二篇 解题技巧篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》贵州省毕节市2021-2022学年高二上学期期末教学质量检测数学(文)试题江西省景德镇一中2022-2023学年高二(18班)上学期期中考试数学试题山东省菏泽市鄄城县第一中学2023-2024学年高一下学期4月月考数学试题