1 . 南北朝时代的伟大科学家祖暅提出体积计算原理:“幂势既同,则积不容异”. 意思是:夹在两个平行平面之间的两个几何体,被平行于这两个平面的任意平面所截,如果截得的两个截面的面积总相等,那么这两个几何体的体积相等. 图1中阴影部分是由曲线
、直线
以及
轴所围成的平面图形
,将图形
绕
轴旋转一周,得几何体
. 根据祖暅原理,从下列阴影部分的平面图形绕
轴旋转一周所得的旋转体中选一个求得
的体积为__________ .
![](https://img.xkw.com/dksih/QBM/2017/7/16/1731215586508800/1732912290021376/STEM/6f760edbdaaa4b49a22a872d6f7e836c.png?resizew=136)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://img.xkw.com/dksih/QBM/2017/7/16/1731215586508800/1732912290021376/STEM/6f760edbdaaa4b49a22a872d6f7e836c.png?resizew=136)
![](https://img.xkw.com/dksih/QBM/2017/7/16/1731215586508800/1732912290021376/STEM/8dd9314bbd414c75846e93f1e4ec5fd3.png?resizew=175)
![](https://img.xkw.com/dksih/QBM/2017/7/16/1731215586508800/1732912290021376/STEM/188f2ccca8144dc893ce56e260fe068c.png?resizew=143)
![](https://img.xkw.com/dksih/QBM/2017/7/16/1731215586508800/1732912290021376/STEM/4aab8aee25b84a599a7f9f65fea0c1f1.png?resizew=143)
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2017-07-18更新
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3卷引用:福建省宁德市2016-2017学年高一下学期期末质量检测数学试题