解题方法
1 . 如图,棱锥的底
是一个矩形,
与
交于
,
是棱锥的高,若
,
,
,求棱锥的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147b4db71d69a1ad140ab6c81883f839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a9dd13007eb1dd1a938d1c1f27e1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df3b2901ad26337818f75e81448ebb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/523c8178a08e632987664eda1800bc38.png)
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解题方法
2 . “用一个不垂直于圆锥的轴的平面截圆锥,当圆锥的轴与截面所成的角不同时,可以得到不同的截口曲线”,利用这个原理,小强在家里用两个射灯(射出的光锥视为圆锥)在墙上投影出两个相同的椭圆(图1),光锥的一条母线恰好与墙面垂直.图2是一个射灯投影的直观图,圆锥
的轴截面
是等边三角形,椭圆
所在平面为
,则椭圆
的离心率为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745e0525a41fe2e2a7739c75a942290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4b27f503ce08bc7851006a98f9ce32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
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名校
解题方法
3 . 已知
是球
表面上的点,
平面
若球
的体积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3e0e93b586844f67ca7a3b157dd310.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/523bdb05d8e5de2a84ccedb6db738037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c880085b1eb986f6ce3653337433789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67fb457e8ac0d3ac35e1c668ea138f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3e0e93b586844f67ca7a3b157dd310.png)
您最近一年使用:0次
昨日更新
|
414次组卷
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3卷引用:海南省儋州市2022-2023学年高二上学期期末考试数学试题
海南省儋州市2022-2023学年高二上学期期末考试数学试题河南省信阳高级中学2023-2024学年高一下学期5月期中测试数学试题(二)(已下线)专题6 组合体中的外接与内切问题【练】(高一期末压轴专项)
解题方法
4 . 如图,等腰直角三角形
中,
,
,
是边
上一动点(不包括端点).将
沿
折起,使得二面角
为直二面角,则三棱锥
的外接球体积的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e18b48c0263fbc4cbf072b7662589e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
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解题方法
5 . 如图,点
是棱长为
的正方体
的表面上一个动点,
,
,
平面
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47ed867750dba3df7a4834827f272c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb71f0f687cc6a5806fdf5e5376aca3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a641eb5d8a88d348a24b78001508c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
A.三棱锥![]() | B.存在一点![]() ![]() |
C.动点![]() ![]() | D.五面体![]() ![]() |
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名校
解题方法
6 . 已知菱形
的边长为2,
.将
沿着对角线
折起至
,连结
.设二面角
的大小为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c034ff5ef70e5d48c0a6b83e48024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684c3c84da636f306191b50caf33f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d9e6cb0c83b99d3a2fa38deae7cf80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32838e506490ef1a8969fa9ecf98fbe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d1179a0fe882b0c390ee9c4e2d35ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.若四面体![]() ![]() |
B.四面体![]() |
C.四面体![]() |
D.当![]() ![]() ![]() |
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7 . 已知轴截面为正三角形的圆锥的体积为
,则圆锥的高为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e6a9a9b2ac597426130c04a667ca80.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
8 . 如图所示,在棱长为2的正方体
中,
分别是棱
的中点,点
是棱
上的动点,
.
时,证明:直线
平面
;
(2)若二面角
的大小等于
,求
的值;
(3)记三棱锥
的体积为
,试将
表示为
的函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82d579a717399137b8c6d475d33cd4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de085db8e8960a3c7b6df69c5b336628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a447dc58e10adb7c8014071651e7c9.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4c4a631729b25fa503b8c069bbbdfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270800ba975e87235e8802a631e5f3a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)记三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b03980f99fa0f339388e564466e8b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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9 . 如图,在正四棱锥
中,
为底面
的中心.
,
,求正四棱锥的体积;
(2)若
,
为
的中点, 求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574dc284fb9e74d65cf0c79a978d65de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97be8206012b8d5b1402dfa5e9761196.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd50cf631e459b58b180cdf2f57844c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87827211113fd8f5d1afd793927222d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
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10 . 若一个球的表面积为
,则该球的体积为_____________
.(结果中保留
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e550b2ba82a15c6542c14be0756144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d1d99afa158b4ba4fc0dae562fcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
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