1 . 某一时段内,从天空降落到地面上的雨水,未经蒸发、渗透、流失而在水平面上积聚的深度,称为这个时段的降雨量(单位:
).24小时降雨量的等级划分如下:
在综合实践活动中,某小组自制了一个底面直径为200
,高为300
的圆锥形雨量器.若一次降雨过程中,该雨量器收集的24小时的雨水高度是150
(如图所示),则这24小时的降雨量的等级是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
24小时降雨量(精确到0.1) | … | 0.1~9.9 | 10.0~24.9 | 25.0~49.9 | 50.0~99.9 |
降雨等级 | … | 小雨 | 中雨 | 大雨 | 暴雨 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/4b26aa5d-bd77-48ad-b9cb-df60ec3d4e2a.png?resizew=160)
您最近一年使用:0次
2021-12-21更新
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727次组卷
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3卷引用:江苏省南京市中华中学2021-2022学年高一下学期期末数学试题
名校
2 . 如图所示,在长方体
中,
,点
是
上的一个动点,若平面
交棱
于点
,给出下列命题:其中真命题的是( )
![](https://img.xkw.com/dksih/QBM/2021/8/31/2798193110728704/2799639877918720/STEM/aefe23bf-c09f-4c10-9ce1-5663b22958a7.png?resizew=226)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c160090a33863408ecb668aa849e1a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83c0b8db2205a6815811aa4ff5390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2021/8/31/2798193110728704/2799639877918720/STEM/aefe23bf-c09f-4c10-9ce1-5663b22958a7.png?resizew=226)
A.四棱锥![]() |
B.存在点![]() ![]() ![]() |
C.对于棱![]() ![]() ![]() ![]() ![]() ![]() |
D.存在唯一的点![]() ![]() |
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2021-09-02更新
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11卷引用:江苏省南京市六校2022-2023学年高三上学期12月期末联考数学试题
江苏省南京市六校2022-2023学年高三上学期12月期末联考数学试题河北省衡水市第一中学2022届高三上学期第一次调研数学试题河北省衡水市冀州区第一中学2022届高三上学期期中数学试题(已下线)专题9.1—立体几何—表面积与体积1—2022届高三数学一轮复习精讲精练(已下线)热点08 立体几何-2022年高考数学【热点·重点·难点】专练(新高考专用)辽宁省沈阳市郊联体2021-2022学年高三上学期期中考试数学试题河北省沧州市第一中学2022届高三上学期12月月考数学试题黑龙江省鸡西市鸡东县第二中学2022-2023学年高三上学期第四次模拟考试数学试题湖北省襄阳市第四中学2021-2022学年高一下学期5月月考数学试题陕西省西北工业大学附属中学2022-2023学年高一下学期第二次月考数学试题湖北省恩施州巴东县第一高级中学2023-2024学年高二上学期第五次月考数学试题
名校
解题方法
3 . 如图,在直三棱柱
中,
,
,
,点
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/449d38d9-768c-4c6c-89cc-070fd7c8e22e.png?resizew=151)
(1)证明:
平面
;
(2)已知二面角
的大小为
,求三棱锥
的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/449d38d9-768c-4c6c-89cc-070fd7c8e22e.png?resizew=151)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ea211a573491409cb60f9fbe9a65cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)已知二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5617a404c5a3356753136e5a6b6d51e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ffc3552dd835a9ee6022bb11397a1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
2021-08-24更新
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2卷引用:江苏省南京市鼓楼区2020-2021学年高二下学期期末数学试题
名校
4 . 如图,在四棱锥
中,底面
是边长为2的正方形,
为等边三角形,平面
平面
,点
在线段
上,
,
交于点
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/6/24/2749649983381504/2784070682738688/STEM/7535fcba6c324256964504a39fbb7dd3.png?resizew=234)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2021/6/24/2749649983381504/2784070682738688/STEM/7535fcba6c324256964504a39fbb7dd3.png?resizew=234)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.锐二面角![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2021-08-11更新
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5卷引用:江苏省南京市六校联合体2020-2021学年高二下学期期末数学试题
江苏省南京市六校联合体2020-2021学年高二下学期期末数学试题(已下线)1.4.2 用空间向量研究距离、夹角问题(同步练习)-【一堂好课】2021-2022学年高二数学上学期同步精品课堂(人教A版2019选择性必修第一册) 湖南省邵阳市武冈市第二中学2021-2022学年高二上学期入学考试数学试题陕西省西安南开高级中学2023-2024学年高二上学期9月第一次质量检测数学试题云南省大理白族自治州民族中学2023-2024学年高二上学期10月月考数学试题
名校
5 . 已知菱形
的边长为2,
,现将
沿
折起形成四面体
.设
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2036191be2322003aaee6bb411868327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bfc0387785bf3c60f75ed3d34cc98a.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.无论![]() ![]() ![]() |
D.存在两个不同的![]() ![]() ![]() |
您最近一年使用:0次
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404次组卷
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3卷引用:江苏省南京市“校际联合体”2020-2021学年高一下学期期末联考数学试题
6 . 中国南北朝时期数学家、天文学家祖冲之、祖暅父子总结了魏晋时期著名数学家刘徽的有关工作,提出“幂势既同,则积不容异”.“幂”是截面积,“势”是几何体的高,即:两个等高的几何体若在所有等高处的水平截面的面积相等,则这两个几何体的体积相等,上述原理称为“祖暅原理”.一个上底面边长为1,下底面边长为2,侧棱长为
的正六棱台与一个不规则几何体满足“幂势既同”,则该不规则几何体的体积为( )
![](https://img.xkw.com/dksih/QBM/2021/6/29/2753646430076928/2781059687071744/STEM/e9924314-9fd0-4825-94d4-43a3d14656d4.png?resizew=252)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
![](https://img.xkw.com/dksih/QBM/2021/6/29/2753646430076928/2781059687071744/STEM/e9924314-9fd0-4825-94d4-43a3d14656d4.png?resizew=252)
A.![]() | B.![]() | C.![]() | D.21 |
您最近一年使用:0次
2021-08-07更新
|
934次组卷
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3卷引用:江苏省南京市“校际联合体”2020-2021学年高一下学期期末联考数学试题
名校
解题方法
7 . 如图,在三棱柱
中,侧面
是矩形,侧面
是菱形,M、N分别是
、
的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429228f882da65a8e0064c88d02b8e40.png)
平面
;
(2)求证:
;
(3)若
,
是边长为4的正三角形,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429228f882da65a8e0064c88d02b8e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98faac7a82235d53bb4b6abe7ee54951.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98474425eb86a28f2b01cec95643ae7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcfc6016de043e3885dd8c28d62f219.png)
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4卷引用:江苏省南京市“校际联合体”2020-2021学年高一下学期期末联考数学试题
8 . 已知某圆锥的侧面展开图是一个半径为2的半圆,则该圆锥的体积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-07-19更新
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373次组卷
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3卷引用:江苏省南京市第二十九中学2020-2021学年高一下学期期末数学试题
9 . 如图在三棱柱
中,侧面
为菱形,平面
平面
,直线
与平面
所成线面角为
,且
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/7/2/2755799983292416/2767672589090816/STEM/662c6e9aeaad4957a88fa236836b8f59.png?resizew=218)
(1)求证:平面
平面
;
(2)设
为线段
上一点,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb8e20db1fbb40f17dea52f951b907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a96fd5c137199d2d8e89ce2d7f70c7.png)
![](https://img.xkw.com/dksih/QBM/2021/7/2/2755799983292416/2767672589090816/STEM/662c6e9aeaad4957a88fa236836b8f59.png?resizew=218)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e3a59d7bf91a7540e35ce0011ad9b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,过圆
外一点
作圆的切线
,
,切点分别为A,B,现将
沿
折起到
,使点P在圆
所在平面上的射影为圆心
,若三棱锥
的体积是圆锥
体积的
.则
( )
![](https://img.xkw.com/dksih/QBM/2021/6/25/2750565087543296/2763112209793024/STEM/000dbd41-4e7a-445e-a82f-f639c284fbd8.png?resizew=388)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca15691dfea154b932004966f2fbca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad895b1c422b40c35be89c8bef22e834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef328d61bcf3cece520c35a2ce449ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ca9177aeec1b81a284502cc7491636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63c34ce5d053f39dc18a5d6b0d3685d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63cd54d2010c21f8219c6f43d97f4e40.png)
![](https://img.xkw.com/dksih/QBM/2021/6/25/2750565087543296/2763112209793024/STEM/000dbd41-4e7a-445e-a82f-f639c284fbd8.png?resizew=388)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
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