名校
1 . 如图,在直三棱柱
中,
是棱BC上一点(点D与点
不重合),且
,过
作平面
的垂线
.
;
(2)若
,当三棱锥
的体积最大时,求AC与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9d2462e6dbd321cf3abae25a56adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bcc3c5b41a01362779683f5b70710c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446091491fb55549972f35a206fcab1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5445220e9b81a876e359615859a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
您最近一年使用:0次
7日内更新
|
371次组卷
|
4卷引用:海南省2022-2023学年高二下学期学业水平期中考试数学试题
名校
解题方法
2 . 如图,在长方体
中,
,
,
分别为
,
的中点.
(1)证明:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b7f88edef2dc47d8ffb34aa6f2b64e.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/f9300e39-4f40-41ff-a41c-448cc0a0424a.png?resizew=125)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744b107d639392e48e5cef49b48d6e36.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712e9f65a80502f4e224fe234dbcc316.png)
您最近一年使用:0次
2023-11-20更新
|
283次组卷
|
2卷引用:海南省2023-2024学年高二上学期11月期中阶段性教学检测(一)数学试题
解题方法
3 . 如图,在四棱锥
中,底面
是正方形,
平面
,且
,点
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/bf75dc94-bbb1-470b-bc69-01ec2f5784b5.png?resizew=178)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/bf75dc94-bbb1-470b-bc69-01ec2f5784b5.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82867bb23bc067cce2848092c0222670.png)
您最近一年使用:0次
解题方法
4 . 在四棱锥
中,底面
为矩形,
平面
,点
在线段
上,
平面
.
(1)证明:
平面
;
(2)若
,
,求几何体
的体积.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/9e24b473-b96b-4f50-a47c-abbb9224ae83.png?resizew=162)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42020cfacd62b300cad053981bab9e0b.png)
您最近一年使用:0次
5 . 平面
内
是直角三角形且C是直角顶点,若
.
(1)求证:平面
平面PBC
(2)
是等腰直角三角形且斜边
,
,求棱锥
的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e35f3a470885d88519e1a71db4b323.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/d05a1f82-2465-4779-b9c5-7b428ab45bee.png?resizew=174)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd689863203d6891a6a8ce8b40dd5a90.png)
您最近一年使用:0次
6 . 圆锥的底边半径为3,母线长为5
(1)求它的表面积
(2)求它的体积
(1)求它的表面积
(2)求它的体积
您最近一年使用:0次
名校
解题方法
7 . 如图,在直三棱柱
中,
,D,E分别为
和
的中点.
(1)求证:
平面
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/f0e377f5-2599-4fa9-a87c-911f6e0cf3bb.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92bced6bf70db7229db85f2b10339431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a4075106569eec5da4cb17ddfb57ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
您最近一年使用:0次
2023-07-26更新
|
617次组卷
|
2卷引用:海南省海口市第一中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
8 . 如图,正四棱锥P-ABCD底面正方形的边长为2,侧棱长为
.
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987895386898432/2989966502223872/STEM/201515c1-6c44-4ce8-be5d-9a412bc27acc.png?resizew=230)
(1)求该正四棱锥的表面积;
(2)求该正四棱锥外接球的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987895386898432/2989966502223872/STEM/201515c1-6c44-4ce8-be5d-9a412bc27acc.png?resizew=230)
(1)求该正四棱锥的表面积;
(2)求该正四棱锥外接球的体积.
您最近一年使用:0次
2022-05-29更新
|
634次组卷
|
2卷引用:海南省洋浦中学2022-2023学年高二上学期期中检测数学试题
名校
9 . 如图,在四棱锥
中,
底面
,且
是直角梯形,
,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/11/2892244138704896/2892935540654080/STEM/deaf33d4-e6c7-4007-9138-67042ea0878b.png?resizew=206)
(1)证明:直线
平面
;
(2)者直线
与平面
所成角的正弦值为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca91743fcdc23d0276a543813ec825fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd3c2e2199cd4565c05b949bc21fc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2022/1/11/2892244138704896/2892935540654080/STEM/deaf33d4-e6c7-4007-9138-67042ea0878b.png?resizew=206)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)者直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d492a2248463e0c0199a25d0f76d23.png)
您最近一年使用:0次
2022-01-12更新
|
1023次组卷
|
14卷引用:海南省海口市第四中学2023-2024学年高二上学期第一次月考数学试题
海南省海口市第四中学2023-2024学年高二上学期第一次月考数学试题江西省赣州市赣县第三中学2021-2022学年高二10月月考数学(文)试题(已下线)江苏省南通市如皋市2021-2022学年高二下学期期初调研数学试题四川省攀枝花市第七高级中学校2020-2021学年高二下学期模拟考试数学(理)试题上海市崇明中学2021届高三5月模拟数学试题(已下线)2021年秋季高三数学开学摸底考试卷01(浙江专用)(已下线)考点34 直线、平面垂直的判定及其性质-备战2022年高考数学(理)一轮复习考点帮(已下线)专题04 立体几何-2021年高考真题和模拟题数学(文)分项汇编(全国通用)(已下线)专题04 立体几何-2021年高考真题和模拟题数学(理)专项汇编(全国通用)(已下线)考向22 空间几何体-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)专题18 立体几何综合-备战2022年高考数学(理)母题题源解密(全国乙卷)(已下线)专题19 几何体的表面积与体积问题——备战2022年高考数学二轮复习常考点专题突破(已下线)专题22 盘点空间线面角的问题——备战2022年高考数学二轮复习常考点专题突破江苏省南京师范大学附属实验学校2022-2023学年高一下学期5月月考数学试题