1 . 如图,
是圆柱的底面直径,
是圆柱的母线且
,点
是圆柱底面圆周上的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/7/6f43aeb7-a94c-4106-9c47-14477897d76f.png?resizew=163)
(1)求圆柱的侧面积和体积;
(2)若
,
是
的中点,点
在线段
上,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bee9d35f57e7bd81f397f82a34bbc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/7/6f43aeb7-a94c-4106-9c47-14477897d76f.png?resizew=163)
(1)求圆柱的侧面积和体积;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e47976ad5a87c265c00d8a0937f95f8.png)
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解题方法
2 . 如图,已知长方体
底面是边长为
的正方形,侧棱长为
,有一圆柱以平面
、平面
分别为上下底面,且其侧面与长方体除去平面
、平面
后剩余的四面均相切.点
为平面
截圆柱所得椭圆上的一动点.
![](https://img.xkw.com/dksih/QBM/2021/10/11/2826991532228608/2827553410154496/STEM/042d95c408ce4f2686508430902dd912.png?resizew=190)
(1)求平面
截圆柱所得椭圆的面积;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://img.xkw.com/dksih/QBM/2021/10/11/2826991532228608/2827553410154496/STEM/042d95c408ce4f2686508430902dd912.png?resizew=190)
(1)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3a8a0dfd7605db35891143f4bfc02f.png)
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