1 . 如图,高度均为3的封闭玻璃圆锥和圆柱容器内装入等体积的水,此时水面高度均为
,若
,记圆锥的底面半径为
,圆柱的底面半径为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187de07874b5370c4489cb4a2dff0b1.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e753dc81ed21f878fff89e98cccf24a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187de07874b5370c4489cb4a2dff0b1.png)
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2023-09-09更新
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386次组卷
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3卷引用:2024年北京高考数学真题变式题11-15
2 . 已知一个圆柱与一个圆锥的底面半径相等,圆柱的高等于其底面直径,圆锥的高等于其底面直径的
倍.给出下列结论:
①设圆柱与圆锥的体积分别为
、
,则
;
②设圆柱与圆锥的轴截面面积分别为
、
,则
;
③设圆柱与圆锥的侧面积分别为
、
,则
;
④设圆柱与圆锥表面积分别为
、
,则
.
其中所有正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
①设圆柱与圆锥的体积分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d72c810a808b90a89edfa6839b5ac0.png)
②设圆柱与圆锥的轴截面面积分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3155c43e5ea9d5af8327ca4a856f4105.png)
③设圆柱与圆锥的侧面积分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1587fc507f590e00f03b42749a4e10f.png)
④设圆柱与圆锥表面积分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27182444d3da4003680f07ec299087c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48e81b54f78b96294295542b010dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a89a6b50d9323015c527ee4f7b94b5.png)
其中所有正确结论的序号是( )
A.① | B.②③ | C.①③④ | D.①②③④ |
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