1 . 如图,在四棱锥
中,底面
为等腰梯形,
,
为等腰梯形的高,
,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/e2c68775-a270-46db-81ff-8fcef16f062e.png?resizew=233)
(1)证明:平面
平面
;
(2)求将
以
为旋转轴旋转一周得到的几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6655e2fa64a32cd12fe0279afd65d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdb8041c0cf7f3da0b449f1b282ab36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90311cc187ccac8cb2113ed301582f45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c03559a409275e0de25c861d80916e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df42ded56944398787d0c17744ae3b7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/e2c68775-a270-46db-81ff-8fcef16f062e.png?resizew=233)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb57138eeb7b885bca148a8e869e1d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2a35f6795aed3f3b1a13713df357a4.png)
(2)求将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03a706b08c69fe2daf2e7cc8652d4902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
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名校
解题方法
2 . 已知正方体
的棱长为a,E、F分别为棱
、
的中点,P为体对角线
所在直线上一动点.
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878865860804608/2879476422508544/STEM/04f5074ad4af4ca68c62db8b5f99a97d.png?resizew=226)
(1)作出该正方体过点E、F且和直线
垂直的截面,并证明该截面和直线
垂直;
(2)求出△EFP绕直线EF旋转而成的几何体体积的最小值;
(3)若动点M在直线EF上运动,动点N在平面
上运动,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878865860804608/2879476422508544/STEM/04f5074ad4af4ca68c62db8b5f99a97d.png?resizew=226)
(1)作出该正方体过点E、F且和直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
(2)求出△EFP绕直线EF旋转而成的几何体体积的最小值;
(3)若动点M在直线EF上运动,动点N在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bb1548ddc0e5536a35b1bd78c4e7cd.png)
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2021-12-24更新
|
1008次组卷
|
3卷引用:河南省安阳市第一中学2021-2022学年高一下学期第二次阶段考试数学试题
河南省安阳市第一中学2021-2022学年高一下学期第二次阶段考试数学试题(已下线)第05讲线线、线面、面面垂直的判定与性质(核心考点讲与练)(2)上海市奉贤中学2021-2022学年高二上学期12月月考数学试题
名校
解题方法
3 . 在空间直角坐标系
中,以坐标原点
为圆心,
为半径的球体上任意一点
,它到坐标原点
的距离
,可知以坐标原点为球心,
为半径的球体可用不等式
表示.还有很多空间图形也可以用相应的不等式或者不等式组表示,记
满足的不等式组
表示的几何体为
.
(1)当
表示的图形截
所得的截面面积为
时,求实数
的值;
(2)祖暅原理“幂势既同,则积不容异”.意思是:夹在两个平行平面之间的两个几何体,被平行于这两个平面的任意平面所截,如果截得的两个截面的面积相等,则这两个几何体的体积相等.记
满足的不等式组
所表示的几何体为
请运用祖暅原理求证
与
的体积相等,并求出体积的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80889d020ffcd8dbc2499fe135f82bd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fa0f65abad2a110595a4e5d0229cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a081fb17e159a4378a2414cb1fac1c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7b230f0873760f043aeb5299fabc85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfcff373b650f57e068b74b3356a9f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9c018281fcaaf52863e1f83d9dad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
(2)祖暅原理“幂势既同,则积不容异”.意思是:夹在两个平行平面之间的两个几何体,被平行于这两个平面的任意平面所截,如果截得的两个截面的面积相等,则这两个几何体的体积相等.记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09961db78b0c4ed3ff88c811285142c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8301e48190608ab476dc69ec6a26dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
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