1 . 中国古代数学的瑰宝《九章算术》中记载了一种称为“曲池”的几何体,该几何体是上、下底面均为扇环形的柱体(扇环是指圆环被扇形截得的部分).现有一个如图所示的曲池,
垂直于底面,
,底面扇环所对的圆心角为
,弧
的长度是弧
长度的3倍,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e58edd1f900ca82bb2a3058293f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
A.弧![]() ![]() | B.曲池的体积为![]() |
C.曲池的表面积为![]() | D.三棱锥![]() |
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2024-04-01更新
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969次组卷
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7卷引用:湖北省新高考联考协作体2024届高三下学期2月收心考试数学试题
湖北省新高考联考协作体2024届高三下学期2月收心考试数学试题(已下线)模块五 专题五 全真拔高模拟(高一)(已下线)8.3简单几何体的表面积与体积【第三练】“上好三节课,做好三套题“高中数学素养晋级之路江苏省无锡市辅仁高级中学2023-2024学年高一下学期期中考试数学试题浙江省温州中学2023-2024学年高一下学期期中考试数学试题浙江省杭州外国语学校2023-2024学年高一下学期期中考试数学试卷江苏省无锡市辅仁高级中学2023-2024学年高二下学期期中考试数学试题
名校
解题方法
2 . 如图,已知棱长为2的正方体
,点
是棱
的中点,过点
作正方体
的截面,关于下列判断正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/c1d6f2a7-cf38-4e5f-89d6-1f2e36026aad.png?resizew=166)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/c1d6f2a7-cf38-4e5f-89d6-1f2e36026aad.png?resizew=166)
A.截面的形状可能是正三角形 |
B.截面的形状可能是直角梯形 |
C.此截面可以将正方体体积分成1:3 |
D.若截面的形状是六边形,则其周长为定值 |
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3 . 在四棱锥
中,
是矩形,
为棱
上一点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5130ddc74af23f8ccfaa5974a223e84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
A.点![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.四棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
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名校
解题方法
4 . 在正方体
中,
,
为
的中点,
是正方形
内部一点(不含边界),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/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
A.平面![]() ![]() |
B.平面![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.以![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
5 . 在正棱柱
中,
,点
满足
,其中
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e44cb429eea46e7ee4320147192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6b545127bd51036a5a7b0d3cd5b320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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6 . 已知正四棱柱
的底面边长为1,
,点
在底面
内运动(含边界),点
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da957f6ccc274634a6daa90599449ed3.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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解题方法
7 . 如图,该几何体是由正方形
沿直线
旋转
得到的,已知点
是圆弧
的中点,点
是圆弧
上的动点(含端点),则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12d93bd1130088b622602a6c21c9c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6919ae684f6781571987add69401dbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632049839e056dec120f87fe86fde89e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/f2257834-0640-4408-9615-8e52a8f4446b.png?resizew=161)
A.不存在点![]() ![]() ![]() |
B.存在点![]() ![]() ![]() |
C.存在点![]() ![]() ![]() ![]() |
D.不存在点![]() ![]() ![]() ![]() |
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解题方法
8 . 如图,在正方体
中,
为棱
上的动点,
为棱
的中点,则下列选项正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/d8383a5f-e75c-4e29-b448-4f64e3f7be3b.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/d8383a5f-e75c-4e29-b448-4f64e3f7be3b.png?resizew=160)
A.直线![]() ![]() |
B.当![]() ![]() ![]() ![]() ![]() |
C.不存在点![]() ![]() ![]() ![]() |
D.三棱锥![]() |
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9 . 在四面体
中,棱
的长为
,若该四面体的体积为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829678a17c4ba4653038502bf21d0f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
A.异面直线![]() ![]() ![]() | B.![]() ![]() |
C.点D到平面![]() ![]() | D.当二面角![]() ![]() |
您最近一年使用:0次
2024-03-06更新
|
553次组卷
|
3卷引用:辽宁省名校联盟2023-2024学年高二下学期3月联合考试数学试卷
10 . 在长方体
中,
为
的中点,点
满足
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/eafd9722-5a19-4efb-ac44-0a272b755158.png?resizew=153)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa886db5470a1c77deb23a84d3f82a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d4bde564475d83dcaa454ef160b294.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/eafd9722-5a19-4efb-ac44-0a272b755158.png?resizew=153)
A.若![]() ![]() ![]() |
B.存在点![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次