名校
1 . 在四面体
中,
与
都是边长为6的等边三角形,且二面角
的大小为
,则四面体
外接球的表面积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.52π | B.54π | C.56π | D.60π |
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3卷引用:浙江省杭嘉湖金四县区2022-2023学年高二下学期6月学考模拟考试数学试题
浙江省杭嘉湖金四县区2022-2023学年高二下学期6月学考模拟考试数学试题福建师范大学附属中学2022-2023学年高一下学期期末考试数学试题(已下线)重难点突破01 玩转外接球、内切球、棱切球(二十三大题型)-2
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2 . 已知四棱锥
中,PA⊥平面ABCD,
,
,E为PD中点.
(1)求证:
平面PAB;
(2)设平面EAC与平面DAC的夹角为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becdcd3199ad5f6b9077f4a648f5df02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f86b6bb8d0612e06f5579090727379.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/20/203f38f8-3a48-46ec-9b64-fccb70051cb5.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
(2)设平面EAC与平面DAC的夹角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b565e518d475a50358fedff2f0bb8dec.png)
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5卷引用:浙江省杭嘉湖金四县区2022-2023学年高二下学期6月学考模拟考试数学试题
浙江省杭嘉湖金四县区2022-2023学年高二下学期6月学考模拟考试数学试题河南省周口市川汇区周口恒大中学2023-2024学年高二上学期10月月考数学试题河南省鹤壁市高中2023-2024学年高二上学期12月月考数学试题(已下线)艺体生一轮复习 第七章 立体几何 第36讲 空间向量在立体几何中的应用【练】(已下线)黄金卷01(文科)
3 . 已知圆锥的底面半径为1,其侧面展开图是半圆,则该圆锥的体积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:浙江省杭嘉湖金四县区2022-2023学年高二下学期6月学考模拟考试数学试题
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解题方法
4 . 已知某柱体的三视图如图所示,则该柱体的表面积是( )
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498195691749376/2498648011227136/STEM/5167d394-bea7-4a7b-97b3-efa03913db96.png?resizew=322)
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498195691749376/2498648011227136/STEM/5167d394-bea7-4a7b-97b3-efa03913db96.png?resizew=322)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 如图,六边形
的六个内角均相等,
,M,N分别是线段
,
上的动点,且满足
,现将
,
折起,使得B,F重合于点G,则二面角
的余弦值的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7d8ce787a09b9bb135c0488e5904dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8736715ae88fa4d9ac570a7c9a83f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620e762afe722cc547553805ec8e2ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74682b0dddedd67e31b3ecae3304559d.png)
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498195691749376/2498648011431936/STEM/003116dfdb174e7aac6ba3405088b5fa.png?resizew=366)
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解题方法
6 . 如图,在四棱锥
中,四边形
为梯形,
,且
,
是边长为2的正三角形,顶点
在
上的射影为点
,且
,
,
.
![](https://img.xkw.com/dksih/QBM/2017/5/23/1693201487126528/1694079355232256/STEM/cb25ec6e814f43d69540ba3be48443ff.png?resizew=166)
(1)证明:平面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9742a7f64ff91be02601331f4ef2bb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03952d664fba91020fc5f3bcf2f9746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bd9e8b54864ca44115d24a5aeeb83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc6b661d6eac048285e4faf67e07ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6c3ec6ee03bb1119c5e619d1dd81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1159f900bc18bb46b87f966c1e9bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a0f55bd08d2837ea23bc06b0989419.png)
![](https://img.xkw.com/dksih/QBM/2017/5/23/1693201487126528/1694079355232256/STEM/cb25ec6e814f43d69540ba3be48443ff.png?resizew=166)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cc987fab8fc64dffda0cd31804c9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6c670d0c1af15e4c1ef45d157c89bb.png)
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2017-05-24更新
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6卷引用:浙江省宁波市宁海中学2019-2020学年高二(创新班)下学期高考模拟数学试题