1 . 如图,我们知道,圆锥是
(及其内部)绕
所在的直线旋转一周形成的几何体.我们现将直角梯形
(及其内部)绕
所在的直线旋转一周形成的几何体称为圆台.设
的半径为
,
的半径为
,
.
![](https://img.xkw.com/dksih/QBM/2020/7/15/2506613295849472/2507208684691456/STEM/a5d8434840a64a5f899ff4cc6ac58cc5.png?resizew=293)
(1)求证:圆台的体积
;
(2)若
,
,
,求圆台的表面积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67e3578d543b8f7978beb0440f9e4536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d246fc443cdad4550b22e5d0bf61c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ca3a80eb1552367bb1b7ebebed242e.png)
![](https://img.xkw.com/dksih/QBM/2020/7/15/2506613295849472/2507208684691456/STEM/a5d8434840a64a5f899ff4cc6ac58cc5.png?resizew=293)
(1)求证:圆台的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2c79fe651b63c7efd7f9836d23b099.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e159fa38488741d395ea9cb03386b1ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea196ac1aadb7be4109c02baeadce25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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4卷引用:上海市静安区2019-2020学年高二下学期期末数学试题
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