1 . 我国古代数学著作《九章算术》中记载:斜解立方,得两堑堵.其意思是:一个长方体沿对角面一分为二,得到两个一模一样的堑堵.如图,在长方体
中,
,
,
,将长方体
沿平面
一分为二,得到堑堵
,下列结论正确的序号为______ .
①点C到平面
的距离等于
;
②
与平面
所成角的正弦值为
;
③堑堵
外接球的表面积为
;
④堑堵
没有内切球.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e58edd1f900ca82bb2a3058293f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b14d74bdf9ed7c45b2e754b7ccc4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/203cf047-3c7e-43ff-9a8e-fb0157d5f7d4.png?resizew=233)
①点C到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81365a3726621b6557bd26f3a1a51cae.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588eb9393564a33552c4b2e8de837ca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a24acb11fac4bcf6a86e3e9223a48b.png)
③堑堵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b14d74bdf9ed7c45b2e754b7ccc4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08a01aed02ce1eaf1aaefaa0342b7ad.png)
④堑堵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b14d74bdf9ed7c45b2e754b7ccc4f.png)
您最近一年使用:0次
2 . 《九章算术·商功》:“斜解立方,得两壍堵(qiàn dǔ).斜解壍堵,其一为阳马,一为鳖臑(biē nào).阳马居二,鳖臑居一,不易之率也.”文中所述可用下图表示:
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894203289747456/2895176848777216/STEM/8c0d64b8-e798-4905-a031-747276d8fa23.png?resizew=384)
则几何体“鳖臑”的四个面中,直角三角形的个数为_______ ;若上图中的“立方”是棱长为1的正方体,则
的中点到直线
的距离等于________ .
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894203289747456/2895176848777216/STEM/8c0d64b8-e798-4905-a031-747276d8fa23.png?resizew=384)
则几何体“鳖臑”的四个面中,直角三角形的个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
您最近一年使用:0次