1 . 如图①,是由正三角形
和正方形
组成的平面图形,其中
;将其沿
折起,使得
,如图②所示.
![](https://img.xkw.com/dksih/QBM/2021/1/26/2644559257305088/2646416300343296/STEM/8e42d118-2bbf-47ef-9334-42f57c6c66da.png?resizew=202)
![](https://img.xkw.com/dksih/QBM/2021/1/26/2644559257305088/2646416300343296/STEM/e532ecee-8a3a-4c97-a163-c9a2bf46cf5a.png?resizew=216)
(1)证明:图②中平面
平面
;
(2)在线段
上取一点
,使
,当三棱锥
的体积为
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://img.xkw.com/dksih/QBM/2021/1/26/2644559257305088/2646416300343296/STEM/8e42d118-2bbf-47ef-9334-42f57c6c66da.png?resizew=202)
![](https://img.xkw.com/dksih/QBM/2021/1/26/2644559257305088/2646416300343296/STEM/e532ecee-8a3a-4c97-a163-c9a2bf46cf5a.png?resizew=216)
(1)证明:图②中平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)在线段
![](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/4eac8bfbdcde7e401d1f18f9a476945e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d492a2248463e0c0199a25d0f76d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738bc12c4d44438814ce6f606fda695a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2021-01-29更新
|
1871次组卷
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7卷引用:安徽省宣城市2020-2021学年高三上学期期末数学(文)试题
安徽省宣城市2020-2021学年高三上学期期末数学(文)试题(已下线) 专题18 几何体的表面积与体积的求解 (测)-2021年高三数学二轮复习讲练测(新高考版)(已下线) 专题22 几何体的表面积与体积的求解 (测)-2021年高三数学二轮复习讲练测(文理通用)江西省赣州市南康区唐江中学2021届高三3月综合性考试数学(文)试题苏教版(2019) 必修第二册 过关斩将 章节测试 第13章 立体几何初步(已下线)专题5 综合闯关(提升版)(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
名校
解题方法
2 . 如图,在
中,
,斜边
,半圆
的圆心
在边
上,且与
相切,现将
绕
旋转一周得到一个几何体,点
为圆锥底面圆周上一点,且
.
![](https://img.xkw.com/dksih/QBM/2020/8/6/2522228778729472/2522899826024448/STEM/74f63df1b94d448f8e4a03fcd1bc5338.png?resizew=347)
(1)求球
的半径;
(2)求点
到平面
的距离;
(3)设
是圆锥的侧面与球的交线上一点,求
与平面
所成角正弦值的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdc05e46628a1e9df831e57dd09a703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c276ba2da23cd8c04acf6e317af22df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a0b15556a1584c1b6b2768bbc9cbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d66b83d9dbcb45e1c241d18a3e1843f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdc05e46628a1e9df831e57dd09a703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://img.xkw.com/dksih/QBM/2020/8/6/2522228778729472/2522899826024448/STEM/74f63df1b94d448f8e4a03fcd1bc5338.png?resizew=347)
(1)求球
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce066003c0a1f0879cbca2f32802e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
您最近一年使用:0次
2020-08-07更新
|
2073次组卷
|
7卷引用:上海市七宝中学2019-2020学年高二下学期期末数学试题
上海市七宝中学2019-2020学年高二下学期期末数学试题(已下线)专题8.7 立体几何中的向量方法(练)-2021年新高考数学一轮复习讲练测(已下线)第八单元 立体几何 (A卷 基础过关检测)-2021年高考数学(理)一轮复习单元滚动双测卷上海交通大学附属中学2020-2021学年高二下学期开学考数学试题江苏省南通市海安县曲塘中学2020-2021学年高二上学期阶段性测试二数学试题重庆实验外国语学校2022届高三上学期入学考试数学试题(已下线)专题8.7 立体几何中的向量方法(练)- 2022年高考数学一轮复习讲练测(新教材新高考)
3 . 定义空间点到几何图形的距离为:这一点到这个几何图形上各点距离中最短距离.
(1)在空间,求与定点
距离等于1的点所围成的几何体的体积和表面积;
(2)在空间,线段
(包括端点)的长等于1,求到线段
的距离等于1的点所围成的几何体的体积和表面积;
(3)在空间,记边长为1的正方形
区域(包括边界及内部的点)为
,求到
距离等于1的点所围成的几何体的体积和表面积.
(1)在空间,求与定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)在空间,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)在空间,记边长为1的正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
您最近一年使用:0次
2020-06-12更新
|
1038次组卷
|
9卷引用:上海市虹口区2019-2020学年高二下学期期末数学试题
上海市虹口区2019-2020学年高二下学期期末数学试题(已下线)专题4.5 简单几何体【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)沪教版(2020) 必修第三册 达标检测 第11章 11.4 球沪教版(2020) 必修第三册 同步跟踪练习 第11章 本章测试(已下线)第07讲 基本立体图形与直观图(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)江苏省苏州中学2021-2022学年高一下学期期中数学试题(已下线)11.4球(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)上海市嘉定区第二中学2023-2024学年高二上学期期中数学试题(已下线)8.3简单几何体的表面积与体积——课后作业(基础版)
名校
解题方法
4 . 已知三棱锥
中,
与
均为等腰直角三角形,且
,
,
为
上一点,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/3caa1c6d-ee21-41bb-8761-ecd5664213b7.png?resizew=189)
(1)求证:
;
(2)过
作一平面分别交
,
,
于
,
,
,若四边形
为平行四边形,求多面体
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0870247d35bf60ae14239f608da44759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/3caa1c6d-ee21-41bb-8761-ecd5664213b7.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed21f410e8e459d9bd363a739d37336e.png)
您最近一年使用:0次
2020-05-22更新
|
1309次组卷
|
5卷引用:四川省泸县第五中学2022-2023学年高三上学期期末考试数学(文)试题
解题方法
5 . 如图在四面体
中,
是边长为2的等边三角形,
为直角三角形,其中
为直角顶点,
.
分别是线段
上的动点,且四边形
为平行四边形.
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402334138900480/2402561425956864/STEM/a4d3f4a0e77841beb31ebeef43fec3fc.png?resizew=261)
(1)求证:
平面
,
平面
;
(2)试探究当二面角
从0°增加到90°的过程中,线段
在平面
上的投影所扫过的平面区域的面积;
(3)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9de8916f29934d3ac93e8ab3bf2ab73.png)
,且
为等腰三角形,当
为何值时,多面体
的体积恰好为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0005e1ef60f6ddc5f9a83e3de1ef3b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f562c443af8e9506b3f574f022a55543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab0ed07775b0fdcb368b696a0f65422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27586229847a94bbd04ff726d18a77ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402334138900480/2402561425956864/STEM/a4d3f4a0e77841beb31ebeef43fec3fc.png?resizew=261)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810ee7bc82b6f452afb3fc18691abc3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)试探究当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9de8916f29934d3ac93e8ab3bf2ab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d587ef3b57039cef934efa51729d4aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbdc69d35ac048be3be891555738e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
您最近一年使用:0次
2020-02-19更新
|
495次组卷
|
3卷引用:江西省新余市2019-2020学年高一上学期期末数学试题
6 . 如图,在以
、
、
、
、
、
为顶点的五面体中,
是平行四边形,
,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/e4d63113-d1e7-44ca-b0b9-66f63e8cb321.png?resizew=202)
(1)求证:
;
(2)若
,
,
与平面
所成角为
,求该五面体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386c7de62e8f9a8161ebaefe6b4ec35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07b92b8282c7fd1158b3b5098e38c39.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/e4d63113-d1e7-44ca-b0b9-66f63e8cb321.png?resizew=202)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ff7bf8ffc8a04186e3e13c1a6d5ced.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55dcbe075165566acf363cd199f07ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
您最近一年使用:0次
2019-01-20更新
|
807次组卷
|
3卷引用:【市级联考】四川省雅安市2018-2019学年高二上学期期末考试数学(文)试题
7 . 如图,一简单组合体的一个面ABC内接于圆O,AB是圆O的直径,四边形DCBE为平行四边形,且DC
平面ABC.
(1)证明:平面ACD
平面
;
(2)若
,
,
,试求该简单组合体的体积V.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(1)证明:平面ACD
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
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7卷引用:江苏省南京师范大学附属中学2019-2020学年高一下学期期末模拟数学试题
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