名校
解题方法
1 . 如图,四棱锥
中,底面ABCD为直角梯形.
,
,
,
,
为等边三角形,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/e431c863-ccb6-4fc8-bd6b-3a1bcacd7239.png?resizew=196)
(1)若M为PB的中点,证明:
面PAD;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e70d5be99ab8b058ff2fb4d8c3d0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2970d638e7993b609106d2ddd65e591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5de3b01f3c591a845ffa206675b882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4020b47658346639e42836fea8e672c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2c4cc37d6ba218107c9c5d820740fc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/e431c863-ccb6-4fc8-bd6b-3a1bcacd7239.png?resizew=196)
(1)若M为PB的中点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa14afe6f0aad22e8e869c39a60be657.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df34afa61d3324211e4cba4fc4bf2e4d.png)
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2022-10-21更新
|
615次组卷
|
3卷引用:广西南宁市2023届高三上学期摸底测试数学(文)试题
解题方法
2 . 如图,四棱锥P-ABCD的底面ABCD为正方形,PA⊥平面ABCD,
,点M,N分别是棱PD的三等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/be037f56-d1d5-46a8-bf83-d1be1084582d.png?resizew=184)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
平面ACM;
(2)求三棱锥N-ACM的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0e16456279222b65eda97612acba77.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/be037f56-d1d5-46a8-bf83-d1be1084582d.png?resizew=184)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be82d01e50ab2526de340bf79ceb9471.png)
(2)求三棱锥N-ACM的体积.
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2022-10-20更新
|
615次组卷
|
4卷引用:贵州省遵义市绥阳县2022-2023学年高二上学期第一次联考数学试题
贵州省遵义市绥阳县2022-2023学年高二上学期第一次联考数学试题青海省西宁市大通回族土族自治县2022-2023学年高二上学期期末考试数学(文)试题(已下线)第31讲 空间几何体体积及点到面的距离问题4种题型(已下线)2023年高考全国乙卷数学(文)真题变式题16-20
3 . 《九章算术》是我国古代内容极为丰富的数学名著,书中有如下问题:“今有委米依垣内角,下周八尺,高五尺.问:积及为米几何?”其意思为:“在屋内墙角处堆放米(如图,米堆为一个圆锥的四分之一),米堆底部的弧长为8尺,米堆的高为5尺,问米堆的体积和堆放的各为多少?”已知1斛米的体积约为1.62立方尺,圆周率约为3.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/a762a285-23ca-4629-b217-9421ff673e63.png?resizew=196)
(1)请估算出堆放的米约有多少斛?
(2)若要建造一个底部直径为4尺的家用圆柱形储粮仓,试问储粮仓的高至少为多少尺,才可以将这堆米全部放入?(结果均保留整数)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/a762a285-23ca-4629-b217-9421ff673e63.png?resizew=196)
(1)请估算出堆放的米约有多少斛?
(2)若要建造一个底部直径为4尺的家用圆柱形储粮仓,试问储粮仓的高至少为多少尺,才可以将这堆米全部放入?(结果均保留整数)
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2022-10-20更新
|
337次组卷
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4卷引用:上海海事大学附属北蔡高级中学2022-2023学年高二上学期10月月考数学试题
上海海事大学附属北蔡高级中学2022-2023学年高二上学期10月月考数学试题上海市曹杨中学2022-2023学年高二上学期期中数学试题(已下线)11.2锥体(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020必修第三册)(已下线)专题8.6 简单几何体的表面积与体积(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
4 . 如图所示,在四棱柱
中,底面
是等腰梯形,
,
,
,侧棱
⊥底面
且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/f44ca6e0-bf5d-4599-bfdf-ff928725ac24.png?resizew=173)
(1)指出棱
与平面
的交点
的位置(无需证明);
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7ddbb49c644bf06ccbad885ba2c84a.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/7db886994f0a7ddfeb0fe2d7099d4498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8781b3e04f90bde1fd8a96075ab932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161f651ef002ac85870d46b04347b54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5493b3fbfbf3d2ec8c57fe228d8047cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/f44ca6e0-bf5d-4599-bfdf-ff928725ac24.png?resizew=173)
(1)指出棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb16f7dbc4b9993c4efa0764df1d8ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c66600644e8bdff1728bf2c7e5375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c66600644e8bdff1728bf2c7e5375.png)
您最近一年使用:0次
2022-10-19更新
|
480次组卷
|
3卷引用:广西2022届高三高考桂柳鸿图综合模拟金卷(2)数学(文)试题
名校
5 . 如图所示,圆锥SO的底面圆半径
,母线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/7eb2a967-f90b-4d58-98c4-4910fdc0ac9a.png?resizew=149)
(1)求此圆锥的体积和侧面展开图扇形的面积;
(2)过点O在圆锥底面作OA的垂线交底面圆圆弧于点P,设线段SO中点为M,求异面直线AM与PS所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2057edff5cd4864dc53c3b52805ba117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e456265c35938ebef2fb65cda3dd69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/7eb2a967-f90b-4d58-98c4-4910fdc0ac9a.png?resizew=149)
(1)求此圆锥的体积和侧面展开图扇形的面积;
(2)过点O在圆锥底面作OA的垂线交底面圆圆弧于点P,设线段SO中点为M,求异面直线AM与PS所成角的大小.
您最近一年使用:0次
2022-10-19更新
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328次组卷
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3卷引用:上海市徐汇区2019-2020学年高三上学期第一次模拟数学试题
6 . 在四棱锥P-ABCD中,底面是边长为2的菱形,
,对角线AC与BD相交于点O,PO⊥平面ABCD,PB与平面ABCD所成的角为60°.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/f69856cb-34ac-4ffe-a56f-7d4cfd45f3cf.png?resizew=185)
(1)求四棱锥P-ABCD的体积;
(2)若E是PB的中点,求异面直线DE与PA所成角的余弦值;
(3)求二面角C-PB-D的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e15be0b520fbe4fbceaddf4b5ade06.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/f69856cb-34ac-4ffe-a56f-7d4cfd45f3cf.png?resizew=185)
(1)求四棱锥P-ABCD的体积;
(2)若E是PB的中点,求异面直线DE与PA所成角的余弦值;
(3)求二面角C-PB-D的正切值.
您最近一年使用:0次
2022-10-17更新
|
306次组卷
|
4卷引用:专题25 二面角相关问题训练-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)
(已下线)专题25 二面角相关问题训练-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)四川省遂宁中学校2022-2023学年高二上学期9月月考数学(理)试题江西省赣州市赣县第三中学2022-2023学年高二上学期开学考试数学试题(已下线)第19讲 空间图形的表面积和体积
名校
解题方法
7 . 如图,AB是圆柱的底面直径,AB=2,PA是圆柱的母线且PA=2,点C是圆柱底面圆周上的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/ea1ef0aa-b54e-40c8-a6de-89b11f418c1f.png?resizew=177)
(1)求圆柱的侧面积和体积;
(2)若AC=1,D是PB的中点,点E在线段PA上,求CE+ED的最小值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/ea1ef0aa-b54e-40c8-a6de-89b11f418c1f.png?resizew=177)
(1)求圆柱的侧面积和体积;
(2)若AC=1,D是PB的中点,点E在线段PA上,求CE+ED的最小值.
您最近一年使用:0次
2022-10-17更新
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553次组卷
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6卷引用:上海市行知中学2018-2019学年高二下学期期中数学试题
8 . 如图,四边形
为菱形,
是平面
同一侧的两点,
平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/6e5ff551-f963-4013-a45a-3d1cc6484c4a.png?resizew=187)
(1)证明:平面
平面
;
(2)求四棱锥
与四棱锥
公共部分的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51cdede506fc850f6714ec472aeb121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be01760a2aa3084f1b8b8df67e67965d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def96a65cce4cafc1e6a6a24bd54a200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d475c62cf3690c78b37a2b59e3f243e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/6e5ff551-f963-4013-a45a-3d1cc6484c4a.png?resizew=187)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff0e0fbc31a6bc4b20cfb2c33e0e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a0d238b6e9b49bbea22a79402e8e4f.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34295a80212129405593c3bac51aef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b998691dd4d8fc9dfebd3b095ed51.png)
您最近一年使用:0次
9 . 如图,在多面体
中,四边形
是正方形,
平面
,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/ec19cdba-eec0-4ae9-999f-7a4454aba794.png?resizew=212)
(1)求多面体
体积的最大值;
(2)若
,求直线
与平面
所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a38e6c6dfde2b19b6b47f35a439a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d740c5dcc2122cb8767b512abb429f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a989aa942219970ec11ccd6ab186d69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0f24915e2c414825b0f9a304e106fa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/ec19cdba-eec0-4ae9-999f-7a4454aba794.png?resizew=212)
(1)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ce838f38419e8781d63b3417cac5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
您最近一年使用:0次
解题方法
10 . 如图,已知三棱锥A-BCD的体积为2,棱AB,AC,AD两两垂直,AB=AC=2.点E是BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/b1af1a7f-a5ca-4808-bcf9-a50efceec940.png?resizew=151)
(1)求棱AD的长:
(2)求直线AE与平面BCD所成角的大小,(用反三角函数值表示)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/b1af1a7f-a5ca-4808-bcf9-a50efceec940.png?resizew=151)
(1)求棱AD的长:
(2)求直线AE与平面BCD所成角的大小,(用反三角函数值表示)
您最近一年使用:0次