解题方法
1 . 祖暅(公元5—6世纪,祖冲之之子),是我国齐梁时代的数学家,他提出了一条原理:“幂势既同,则积不容异.”这句话的意思是:两个等高的几何体若在所有等高处的水平截面的面积相等,则这两个几何体的体积相等.如图将底面直径皆为
,高皆为
的椭半球体和已被挖去了圆锥体的圆柱体放置于同一平面
上,用平行于平面
且与
距离为
的平面截两个几何体得到
及
两截面,可以证明
总成立,若椭半球的短轴
,长半轴
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/2/19/2919607826079744/2924797869096960/STEM/8c870d00-2ab2-489d-b8ff-3db9dbcb9513.png?resizew=422)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18436f0e2391b0ab7537a566fc28204c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ef0cd8fc26307d24ac98ea0556464a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173d3e1ca62e4825252dddecbefe7b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009467e7d7de6caeb1eb01210ccb71ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b515965c22d2950b592c096c6e3bdfd4.png)
![](https://img.xkw.com/dksih/QBM/2022/2/19/2919607826079744/2924797869096960/STEM/8c870d00-2ab2-489d-b8ff-3db9dbcb9513.png?resizew=422)
A.椭半球体的体积为30π |
B.椭半球体的体积为15π |
C.如果![]() ![]() ![]() ![]() ![]() |
D.如果![]() ![]() ![]() ![]() ![]() |
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