1 . 攒尖是我国古代建筑中屋顶的一种结构样式,多见于亭阁式建筑、园林建筑.如图所示的带有攒尖的建筑屋顶可近似看作一个圆锥,其侧面展开图是一个圆心角为120°、半径为
的扇形,则该屋顶的体积约为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 某烟花厂准备生产一款环保、安全的迷你小烟花,初步设计了一个平面图,如图所示,该平面图由
,直角梯形
和以
为圆心的四分之一圆弧
构成,其中
,
,
,且
,
,
,将平面图形
以
所在直线为轴,旋转一周形成的几何体即为烟花.
(2)工厂准备将矩形
(该矩形内接于图形
,
在弧
上,
在线段
上,
在
上)旋转所形成的几何体用来安放燃料,设
(
),
①请用
表示燃料的体积
;
②若烟花燃烧时间
和燃料体积
满足关系
,请计算这个烟花燃烧的最长时间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ca082df4cfac078e6b0e254000a5660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed1321e4081133b1a8bbe994ecac48a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcbde67cc84757b10bb66c47cee22de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be082aedbea135ea8fdcadca2cf427b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aaf670a0170e85aeffdc41d71cc975e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0761165f1176f3a5fe4f7b052832316d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc04ed25823067a16e7e32a43442cfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)工厂准备将矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec780e86f57790cf88ec761e219bf5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62fbf288f38b71a82d245dabcd8a057c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e753174fb1caad7e8f56bf8697b8b6a.png)
①请用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
②若烟花燃烧时间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f146473edca969234a9514c1bc5582fe.png)
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2023-07-12更新
|
739次组卷
|
7卷引用:重组2 高一期末真题重组卷(山东卷)B提升卷
(已下线)重组2 高一期末真题重组卷(山东卷)B提升卷(已下线)第六章 突破立体几何创新问题 专题二 融合科技、社会热点 微点3 融合科技、社会热点等现代文化的立体几何和问题综合训练【培优版】山东省淄博第六中学2023-2024学年高一下学期期中考试数学试题(已下线)专题03 基本立体图形、直观图、表面积与体积-期末真题分类汇编(新高考专用)山东省日照市2022-2023学年高一下学期期末校际联合考试数学试题福建省泉州第五中学2023-2024学年高一下学期期中考试数学试题(已下线)专题04 立体几何初步-期期末真题分类汇编(人教A版2019必修第二册)
解题方法
3 . 如图,在棱长为4的正方体
中,
,
分别是
、
中点,点
是线段
上的动点,则三棱锥
的体积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90da0522dd9378bab25de2f560aec563.png)
A.![]() | B.![]() | C.![]() | D.与点P的位置有关 |
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