解题方法
1 . 正三棱锥(底面是正三角形,顶点在底面投影是底面中心)的高为1,底面边长为
,正三棱锥内有一个球与其四个面相切,则此球表面积是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
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解题方法
2 . 如图,已知边长为4的菱形
中,
,将
沿对角线
翻折至
所在的位置,若二面角
的大小为
,则过
,
,
,
四点的外接球的表面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f6bf45ecba77a2581e1142bd16bf8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951609a31601ae3944aba9684de61142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/866ac361-ed8d-4164-a0dc-57f73878beef.png?resizew=261)
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解题方法
3 . 已知图1中的正三棱柱
的底面边长为2,体积为
,去掉其侧棱,将上底面绕上、下底面的中心所在的直线
,逆时针旋转
后(下底面位置保持不变),再添上侧棱,得到图2所示的几何体,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759898787160064/2778264565530624/STEM/1cd42021-82a6-422e-a0e0-a0eb84b661a3.png?resizew=444)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe639eab78eafd2d40ea70aa5d3f21d.png)
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759898787160064/2778264565530624/STEM/1cd42021-82a6-422e-a0e0-a0eb84b661a3.png?resizew=444)
A.![]() |
B.![]() |
C.四边形![]() |
D.正三棱柱![]() ![]() |
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