1 . 如图所示,正六棱锥的底面边长为4,H是
的中点,O为底面中心,
.
(2)求六棱锥的表面积和体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251a6d3a78b742f1ef91b2b3cf8c0f3d.png)
(2)求六棱锥的表面积和体积.
您最近一年使用:0次
2023-09-07更新
|
590次组卷
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9卷引用:贵州省黄平县且兰高级中学2023-2024学年高二上学期第一次月考数学试题
贵州省黄平县且兰高级中学2023-2024学年高二上学期第一次月考数学试题福建省厦门第二中学2022-2023学年高一下学期4月阶段性考试数学试题内蒙古呼和浩特市第二中学2023-2024学年高二上学期10月月考数学试题(已下线)专题09 简单几何体的表面积与体积(七大考点)-【寒假自学课】(人教A版2019)上海师范大学附属中学2023-2024学年高二上学期期末考试数学试题(已下线)第04讲 8.3.1 棱柱、棱锥、棱台的表面积和体积-【帮课堂】(人教A版2019必修第二册)(已下线)专题15 简单几何体的表面积与体积-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)8.3.1 棱柱、棱锥、棱台的表面积和体积-同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)11.1.6 祖暅原理与几何体的体积-【帮课堂】(人教B版2019必修第四册)
2 . 如图,某几何体的下部分是长、宽均为8,高为3的长方体,上部分是侧棱长都相等且高为3的四棱锥,求:
(2)若要将几何体下部分表面刷上涂料(除底面),求需要刷涂料的表面积.
(2)若要将几何体下部分表面刷上涂料(除底面),求需要刷涂料的表面积.
您最近一年使用:0次
2023-09-21更新
|
736次组卷
|
7卷引用:贵州省黄平县且兰高级中学2023-2024学年高二上学期第一次月考数学试题
贵州省黄平县且兰高级中学2023-2024学年高二上学期第一次月考数学试题新疆柯坪县柯坪湖州国庆中学2022-2023学年高二上学期12月月考数学试题上海市复兴高级中学2023-2024学年高二上学期期中数学试题8.3.1.2棱柱、棱锥、棱台的体积练习(已下线)专题8.10 立体几何初步全章十三大基础题型归纳(基础篇)-举一反三系列(已下线)模块三 专题5 大题分类练(空间几何体表面积和体积)(人教A版)(已下线)第8.3.1讲 棱柱、棱锥、棱台的表面积和体积-同步精讲精练宝典(人教A版2019必修第二册)
解题方法
3 . 已知ABCD是边长为2的正方形,平面
平面DEC,直线AE,BE与平面DEC所成的角都为45°.
![](https://img.xkw.com/dksih/QBM/2021/11/18/2854152125972480/2861941634793472/STEM/2c0f360e744247acbdc48ea7ad5bfe81.png?resizew=214)
(1)证明:
.
(2)求四棱锥E-ABCD的体积V.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://img.xkw.com/dksih/QBM/2021/11/18/2854152125972480/2861941634793472/STEM/2c0f360e744247acbdc48ea7ad5bfe81.png?resizew=214)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0aaa5cf7dafac1b64eafe84cae5674.png)
(2)求四棱锥E-ABCD的体积V.
您最近一年使用:0次
2021-11-29更新
|
315次组卷
|
2卷引用:贵州省毕节市金沙县2022届高三11月月考数学(文)试题
名校
解题方法
4 . 已知菱形
的边长为
,
,如图1.沿对角线
将
向上折起至
,连接
,构成一个四面体
,如图2.
;
(2)若
,求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c967c9b3f669ea78edd838e1d8b59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685534ba47e83433200ce29660875118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
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2021-11-13更新
|
1017次组卷
|
7卷引用:贵州省贵州师范大学附属中学2021-2022学年高二10月月考数学(理)试题
名校
解题方法
5 . 在长方体
中,AB=6,BC=8,
.
(1)求三棱锥
的体积;
(2)在三棱柱
内放一个体积为V的球,求V的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d0fdc5a00ca0e857b89a7e1420df29.png)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ebd86a076448d19401268f139b5b90.png)
(2)在三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
您最近一年使用:0次
6 . 已知圆台的上下底面半径分别为
,母线长为
.求:
(1)圆台的高;
(2)圆台的体积.
注:圆台的体积公式:
,其中
,S分别为上下底面面积,h为圆台的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1eb7fd83811eadd44317029a0f6eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
(1)圆台的高;
(2)圆台的体积.
注:圆台的体积公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ca9e4f983b8b70755c0f781e390a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150a135bbd528daf3f19a58a621a57c6.png)
您最近一年使用:0次
2020-12-16更新
|
401次组卷
|
5卷引用:贵州省平塘民族中学2021-2022学年高二上学期第一次月考数学试题
7 . 如图,在四棱锥P-ABCD中,
为正三角形,四边形ABCD为矩形,且平面PAB⊥平面ABCD,AB=2,PC=4
![](https://img.xkw.com/dksih/QBM/2020/12/7/2609273135898624/2611427598327808/STEM/aa3685c72352404cb37106ddc569c4c3.png?resizew=154)
(1)求证:平面PAB⊥平面PAD
(2)若点M是PD的中点,求三棱锥P-ABM的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://img.xkw.com/dksih/QBM/2020/12/7/2609273135898624/2611427598327808/STEM/aa3685c72352404cb37106ddc569c4c3.png?resizew=154)
(1)求证:平面PAB⊥平面PAD
(2)若点M是PD的中点,求三棱锥P-ABM的体积
您最近一年使用:0次
2020-12-10更新
|
393次组卷
|
2卷引用:贵州省贵阳市第一中学2021届高考适应性月考卷(三)文科数学试题
8 . 如图,在三棱柱
中,侧棱垂直于底面,
,
,
,
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/c9b84af2-2abc-42fc-b395-2dbd41e2f3c9.png?resizew=122)
(1)求证:平面
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/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cfb38323095090b0fe5eee70b24210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.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/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/c9b84af2-2abc-42fc-b395-2dbd41e2f3c9.png?resizew=122)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
您最近一年使用:0次
2020-12-02更新
|
487次组卷
|
3卷引用:贵州省六盘水市第二中学2022-2023学年高二上学期9月月考数学试题
名校
解题方法
9 . 如图,在四棱锥
中,平面
平面
,底面
为梯形,
,
,且
与
均为等边三角形,
为
的中点,
为
的外心.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/2d3f30a6-ac4a-4650-957a-9d74248c0bc8.png?resizew=188)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7c4762381fa5fb173866d31b749d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e1441a49e782ff0ef46e776cde06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/2d3f30a6-ac4a-4650-957a-9d74248c0bc8.png?resizew=188)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05952cdf83c61053d809ce3f4487e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c440fdd6a9db8fcbf6584dd03d0140a6.png)
您最近一年使用:0次
10 . 如图,四棱柱
的底面是直角梯形,
,
,
,四边形
和
均为正方形.
![](https://img.xkw.com/dksih/QBM/2020/2/9/2395195597750272/2395577642475520/STEM/d3415e3448824938887b5ba46d998f84.png?resizew=269)
(1)证明:平面
平面
.
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25eb757d05fbff80d50c3bb8dbcb8657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://img.xkw.com/dksih/QBM/2020/2/9/2395195597750272/2395577642475520/STEM/d3415e3448824938887b5ba46d998f84.png?resizew=269)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc8946b35564cd277227b80ef05c7f5.png)
您最近一年使用:0次
2020-02-09更新
|
442次组卷
|
3卷引用:2020届贵州省贵阳市高三11月联合考试数学(文)试题