1 . 如图,等腰直角三角形
的斜边
为正四面体
的侧棱,
直角边
绕斜边
旋转一周,在旋转的过程中,有下列说法:
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841770020675584/2841804122144768/STEM/2b9e5747-b018-4859-8a58-e36efc41b097.png?resizew=223)
①三棱锥
体积的最大值为
,
②三棱锥
体积的最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345d4d7d64d96f835e88b3de3bb0ec91.png)
③存在某个位置,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c51c25b65a37b676ae3c3b71c29f9b.png)
④设二面角
的平面角为
,且
,则
.
其中所有正确说法的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbb48c435c1ea5452cd9c9dd05e53ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2021/11/1/2841770020675584/2841804122144768/STEM/2b9e5747-b018-4859-8a58-e36efc41b097.png?resizew=223)
①三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42020cfacd62b300cad053981bab9e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99790fada481e8b0a4b114b823542a78.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42020cfacd62b300cad053981bab9e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345d4d7d64d96f835e88b3de3bb0ec91.png)
③存在某个位置,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c51c25b65a37b676ae3c3b71c29f9b.png)
④设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d87b527147cb8dbb475bcefc0da2e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcadd1781ee9177e9bc76ce48afdd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abb81a7b51de6e6293064ecf98e0759.png)
其中所有正确说法的序号是( )
A.①③ | B.①④ | C.②③ | D.②④ |
您最近一年使用:0次
解题方法
2 . 已知某几何体的三视图如下所示,现有如下说法:
![](https://img.xkw.com/dksih/QBM/2021/5/25/2728772013023232/2731982409433088/STEM/71d449dd-daf1-4956-bb1e-ee3d1c4bd6c2.png?resizew=241)
①该几何体的最长棱长为
;
②该几何体的体积为2;
③该几何体的表面积为
,
则其中所有正确说法的序号是( )
![](https://img.xkw.com/dksih/QBM/2021/5/25/2728772013023232/2731982409433088/STEM/71d449dd-daf1-4956-bb1e-ee3d1c4bd6c2.png?resizew=241)
①该几何体的最长棱长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
②该几何体的体积为2;
③该几何体的表面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f77350083606561739c277fffe9eb6.png)
则其中所有正确说法的序号是( )
A.③ | B.①② | C.①③ | D.①②③ |
您最近一年使用:0次
名校
3 . 有一个四锥形铅垂,其底面直径为10cm,母线长为15cm.P是铅垂底面圆周上一点,则关于下列命题:①铅垂的侧面积为
;②一只蚂蚁从P点出发沿铅垂侧面爬行一周、最终又回到P点的最短路径的长度为
cm,其中正确的判断是( )
![](https://img.xkw.com/dksih/QBM/2022/4/15/2958919622688768/2961645715333120/STEM/adbbcda2-d50a-4d11-b26e-ae200352c36f.png?resizew=129)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0a3df0d2d0e5bb4f1811ff61ca3813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14fc6d812e0f2a7ff2b7bb4f4c92369d.png)
![](https://img.xkw.com/dksih/QBM/2022/4/15/2958919622688768/2961645715333120/STEM/adbbcda2-d50a-4d11-b26e-ae200352c36f.png?resizew=129)
A.①②都正确 | B.①错误、②正确 |
C.①正确、②错误 | D.①②都错误 |
您最近一年使用:0次
2022-04-19更新
|
600次组卷
|
2卷引用:河南省郑州市十校2021-2022学年高一下学期期中联考数学试题
名校
解题方法
4 . 有一个圆锥形铅垂,其底面直径为10cm,母线长为15cm.P是铅垂底面圆周上一点,则关于下列命题:①铅垂的侧面积为150cm2;②一只蚂蚁从P点出发沿铅垂侧面爬行一周、最终又回到P点的最短路径的长度为
cm.其中正确的判断是( )
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897872790519808/2899176186249216/STEM/05f550a3-8e0f-476c-bc68-976af6082273.png?resizew=132)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14fc6d812e0f2a7ff2b7bb4f4c92369d.png)
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897872790519808/2899176186249216/STEM/05f550a3-8e0f-476c-bc68-976af6082273.png?resizew=132)
A.①②都正确 | B.①正确、②错误 | C.①错误、②正确 |
您最近一年使用:0次
名校
5 . 如图,棱长为2的正方体
中,P、Q分别是面对角线
与BD上的动点,且
,给出下列两个判断:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/fe8a16dc-b5f2-4e71-9700-68a0066edf69.png?resizew=164)
(1)PQ和
始终是异面直线;
(2)PQ长的最小值是
;
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/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7b64a0de3cbdfe5d348041d27e1179.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/fe8a16dc-b5f2-4e71-9700-68a0066edf69.png?resizew=164)
(1)PQ和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
(2)PQ长的最小值是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
则下列说法正确的是( )
A.(1)正确,(2)错误 | B.(1)错误,(2)正确 |
C.(1)正确,(2)正确 | D.(1)错误,(2)错误 |
您最近一年使用:0次