解题方法
1 . 已知某圆锥的轴截面是面积为
的等边三角形,球O内切于该圆锥.
(1)求该圆锥的高;
(2)求内切球O的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求该圆锥的高;
(2)求内切球O的体积.
您最近一年使用:0次
2020-04-24更新
|
859次组卷
|
5卷引用:安徽省池州市2019-2020学年高二上学期期末理科数学试题
名校
解题方法
2 . 如图,某公司制造一种海上用的“浮球”,它是由两个半球和一个圆柱筒组成,其中圆柱筒的高
为2米,球的半径
为0.5米.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/94e4e1ec-0d72-4ff8-a36d-43d979fd0c84.png?resizew=261)
(1)求“浮球”的体积(结果精确到0.1立方米);
(2)假设该“浮球”的建造费用仅与其表面积有关,已知圆锥形部分每平方米建造费用为20元,半球形部分每平方米建造费用为30元,求该“浮球”的建造费用(结果精确到1元).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/94e4e1ec-0d72-4ff8-a36d-43d979fd0c84.png?resizew=261)
(1)求“浮球”的体积(结果精确到0.1立方米);
(2)假设该“浮球”的建造费用仅与其表面积有关,已知圆锥形部分每平方米建造费用为20元,半球形部分每平方米建造费用为30元,求该“浮球”的建造费用(结果精确到1元).
您最近一年使用:0次
2020-02-29更新
|
128次组卷
|
3卷引用:上海市曹杨二中2019-2020学年高二上学期期末数学试题
3 . 如图,把长为6,宽为3的矩形折成正三棱柱
,三棱柱的高度为3,矩形的对角线和三棱柱的侧棱
、
的交点记为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/3630cbe7-2673-4a79-8842-0d68cd22315c.png?resizew=295)
(1)在三棱柱
中,若过
三点作一平面,求截得的几何体
的表面积;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/3630cbe7-2673-4a79-8842-0d68cd22315c.png?resizew=295)
(1)在三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62561476aa60509bde150ae95709d1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5b0e0ca60e90e56a33bedfd48e9802.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c6f95346788277fa68e8408f6bada93.png)
您最近一年使用:0次
2020-02-27更新
|
275次组卷
|
4卷引用:四川省内江市2019-2020学年高二上学期期末数学(文)试题
4 . 如图,在多面体ABCDE中,
,
平面ABC,
,
,
,F为BC的中点,且
.
(1)求证:
平面ADF;
(2)求多面体ABCDE的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d7bd6df0e94731edb8f4649903de73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e405b53cf66f14c54e9ae1e2a013f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508f8d607c633e9b008d48ac3dcd22e2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/17/1b918c3b-eb0b-4714-8cea-a74d779d4793.png?resizew=135)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
(2)求多面体ABCDE的体积.
您最近一年使用:0次
2020-02-24更新
|
233次组卷
|
2卷引用:重庆市第八中学2018-2019学年高二上学期期末(文)数学试题
名校
解题方法
5 . 如图,梯形
所在的平面与等腰梯形
所在的平面互相垂直,
,
,
为
的中点.
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/ee01d5d0-ace5-49d2-bf8d-6c0683e82a1b.png?resizew=159)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9518d0a9119d9416b5198086dd724dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc9204cfa7929a2a72a46e701642ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/ee01d5d0-ace5-49d2-bf8d-6c0683e82a1b.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2d28f1e7a6b17401c19c34beddcbe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac3bbe7410b0176a1b3f9410ab761be.png)
(3)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8192ca9367bc6d502779f123ad3c4b06.png)
您最近一年使用:0次
2020-02-16更新
|
938次组卷
|
4卷引用:四川省乐山市2019-2020学年高二上学期期末数学(文)试题
四川省乐山市2019-2020学年高二上学期期末数学(文)试题四川省泸县第四中学2022-2023学年高二上学期期末考试数学(文)试题江西省南昌市第二中学2021届高三上学期第三次考试数学(文)试题(已下线)专题8.9 《空间向量与立体几何》单元测试卷(测)-2021年新高考数学一轮复习讲练测
6 . 直角梯形
如图放置,已知
,
,
,
.现将梯形
绕直线
旋转一周形成几何体.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/48eb7da4-f824-4029-8aa1-bc03715c3415.png?resizew=97)
(1)画出这个几何体的正视图(不写作法);
(2)求这个几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276f64bcfa74b44c5ef5ca88fc8208f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/48eb7da4-f824-4029-8aa1-bc03715c3415.png?resizew=97)
(1)画出这个几何体的正视图(不写作法);
(2)求这个几何体的体积.
您最近一年使用:0次
15-16高三上·上海浦东新·期中
名校
7 . 如图,在四棱柱
中,侧棱
底面
,
,
,
,
,
,
,(
)
平面
;
(2)若直线
与平面
所成角的正弦值为
,求
的值;
(3)现将与四棱柱
形状和大小完全相同的两个四棱柱拼成一个新的四棱柱,规定:若拼成的新四棱柱形状和大小完全相同,则视为同一种拼接方案,问共有几种不同的拼接方案?在这些拼接成的新四棱柱中,记其中最小的表面积为
,写出
的解析式.(直接写出答案,不必说明理由)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c0ad79161fb29ec231dd0248623ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9740124a284f336f20c98695af04ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5cab760038d20eac10fe6108fbb334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f991c5086ba855802b0331c4e02e3f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223036d27be5914db50fbd5cb19d4212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4e6eb3663870ed202cc208eaf239dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)现将与四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7a84d7e5d6236009a8be655bd500fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7a84d7e5d6236009a8be655bd500fd.png)
您最近一年使用:0次
2020-02-05更新
|
850次组卷
|
5卷引用:北京市一零一中学2021-2022学年高二上学期期末考试数学试题
北京市一零一中学2021-2022学年高二上学期期末考试数学试题(已下线)上海市华东师范大学第二附属中学2020-2021学年高二下学期期中数学试题(已下线)第一章 空间向量与立体几何(压轴必刷30题4种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)上海市华东师大二附中2016届高三上学期期中数学试题辽宁省实验中学2024届高三考前模拟数学试卷
8 . 如图,
是圆柱体
的一条母线,
过底面圆的圆心
,
是圆
上不与
、
重合的任意一点,已知棱
,
,
.
与平面
所成角的大小;
(2)将四面体
绕母线
旋转一周,求
三边旋转过程中所围成的几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)将四面体
![](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/d9f8f01137e92c0f2e63467036ae9cce.png)
您最近一年使用:0次
2020-01-16更新
|
486次组卷
|
6卷引用:专题03空间向量及其应用--高二期末考点大串讲(沪教版2020选修)
(已下线)专题03空间向量及其应用--高二期末考点大串讲(沪教版2020选修)上海市上海交通大学附属中学2021届高三上学期期末数学试题2015届上海市闸北区高三下学期期中练习(二模)理科数学试卷(已下线)上海市华东师大二附中2017-2018学年高三上学期期中数学试题上海市七宝中学2022届高三高考冲刺模拟1数学试题上海市松江二中2023届高三下学期5月月考数学试题
9 . 如图,弧
是半径为r的半圆,
为直径,点E为弧
的中点,点B和点C为线段
的三等分点,线段
与弧
交于点G,平面
外一点F满足
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/22/b806b5ad-5860-4bf3-82a9-47ff13bd946c.png?resizew=246)
(1)求异面直线
与
所成角的大小;
(2)将
(及其内部)绕
所在直线旋转一周形成一几何体,求该几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b5a90e556da12d63b7f481bd8e874c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efdb2104af8e73927f51a7e0a19ede7c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/22/b806b5ad-5860-4bf3-82a9-47ff13bd946c.png?resizew=246)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134a28a0f483a9a534dbe3153c5fa3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
您最近一年使用:0次
2020-01-10更新
|
215次组卷
|
2卷引用:上海市上海中学2017-2018学年高二下学期期末数学试题
名校
10 . 在一个圆锥内作一个内接等边圆柱(一个底面在圆锥的底面上,且轴截面是正方形的圆柱),再在等边圆柱的上底面截得的小圆锥内做一个内接等边圆柱,这样无限的做下去.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/cc8b0e3d-0315-43d4-8340-9eed3f39a9e4.png?resizew=171)
(1)证明这些等边圆柱的体积从大到小排成一个等比数列;
(2)已知这些等边圆柱的体积之和为原来圆锥体积的
,求最大的等边圆柱的体积与圆锥的体积之比.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/cc8b0e3d-0315-43d4-8340-9eed3f39a9e4.png?resizew=171)
(1)证明这些等边圆柱的体积从大到小排成一个等比数列;
(2)已知这些等边圆柱的体积之和为原来圆锥体积的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b37b8b12598827f31495b3182337167.png)
您最近一年使用:0次