名校
解题方法
1 . 记正四棱柱
为
,截面
将正四棱柱
分成两部分,点E,F,G,H分别在棱
,
,
,
上,且
,
,记
,
,
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9458b63a4e8425c6f59e0e37887d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681e6304ec3b733adde692837bf2602a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17eb884c0e7414be81990409dba252f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bc8a47c5268ebfc7329b3398bb9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/463c91e95bf032d464b20f0c53f39d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6125e6e8d7406d54c93512a9fb2cbbe.png)
A.四边形![]() |
B.![]() |
C.若截面![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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2 . 陀螺指的是绕一个支点高速转动的几何体,是中国民间最早的娱乐工具之一,其模型可抽象为圆柱和圆锥的组合体,如图所示.已知EF,BC分别为圆O,
的直径,
,D为弧EF的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/c24d01e0-275a-427f-b537-e39d6897911d.png?resizew=128)
若制作该模型所需原料密度为
,求制作该模型所需的原料质量为________ g;点O到平面ADE的距离为_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23941c9586721aa25a2cc6db00e6e721.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/c24d01e0-275a-427f-b537-e39d6897911d.png?resizew=128)
若制作该模型所需原料密度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69901cad70cb864525ffb0bf8c9b5a.png)
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名校
解题方法
3 . 下列命题正确的有( )
A.空间中两两相交的三条直线一定共面 |
B.已知不重合的两个平面![]() ![]() ![]() ![]() ![]() ![]() |
C.过平面![]() ![]() ![]() ![]() |
D.已知空间中有两个角![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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4 . 如图,圆台
的轴截面为等腰梯形
,
,B为底面圆周上异于A,C的点.
内,过
作一条直线与平面
平行,并说明理由;
(2)设平面
∩平面
,
与平面QAC所成角为
,当四棱锥
的体积最大时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c6d80251fdeabfebd65bca460d55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f664c0db517bec6886ff0b6100fd474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bd886276f8ff9df2a42013b337d726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0c82028e1259f300facd32775a15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c6c1f6d821af7e3c8058993218a861.png)
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2023-02-25更新
|
2330次组卷
|
8卷引用:安徽省合肥一六八中学等学校2024届高三上学期名校期末联合测试数学试题
名校
5 . 已知圆锥SO(O是底面圆的圆心,S是圆锥的顶点)的母线长为
,高为
.若P,Q为底面圆周上任意两点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
A.三角形![]() ![]() |
B.三棱锥![]() ![]() |
C.四面体![]() ![]() |
D.直线SP与平面![]() ![]() |
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2023-02-16更新
|
2042次组卷
|
4卷引用:安徽省合肥市2023届高三下学期第一次教学质量检测数学试题
安徽省合肥市2023届高三下学期第一次教学质量检测数学试题(已下线)专题12空间向量与立体几何(选填题)(已下线)专题05空间几何体的表面积和体积河南省信阳市新县高级中学2024届高三下学期模拟考试一数学试题
名校
解题方法
6 . 已知球O的表面积为
,三棱锥
的顶点都在球面上,该棱锥体积取最大值时下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9c176877b59cd7c34fcc0838b05493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-01-14更新
|
307次组卷
|
3卷引用:安徽省合肥市2022-2023学年高三上学期期末联考数学试题
安徽省合肥市2022-2023学年高三上学期期末联考数学试题安徽省阜阳市临泉第一中学2022-2023学年高三上学期1月期末理科数学试题(已下线)湖南省株洲市2023届高三下学期一模数学试题变式题11-16
名校
7 . 已知直角梯形ABCE中
,
,
,
,
,
,以AD为折痕将
折至
处,得到四棱锥
.
(1)求证:
;
(2)连接AC、BD交于点F,当三棱锥
体积最大时,求点F到平面PCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bbb16f9380dd62d556480a3944be31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0268d04b9dea7629af27af9a0285a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9905e53fd05c87982fced1cc2fc42b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb3e973f4e9361e1d23a0ab56006d12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)连接AC、BD交于点F,当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8a21df84cf292db93b937f4ea47bfe.png)
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