在《九章算术·商功》中,将四个面都为直角三角形的四面体称为鳖臑,如图在鳖臑
中,
平面
,
,
,则鳖臑
内切球的表面积为( )
![](https://img.xkw.com/dksih/QBM/2022/1/25/2902237644988416/2916951566475264/STEM/8da8be19-d8a1-40e1-ad90-eeaef1cd451f.png?resizew=143)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce519312a849963b376c202c3f9d7cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/1/25/2902237644988416/2916951566475264/STEM/8da8be19-d8a1-40e1-ad90-eeaef1cd451f.png?resizew=143)
A.![]() | B.![]() |
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2022·山西吕梁·一模 查看更多[3]
更新时间:2022-02-15 14:56:03
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【知识点】 球的表面积的有关计算
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【推荐1】在《九章算术》中,将四个面都为直角三角形的三棱锥称之为鳖臑,已知鳖臑
的三视图如图所示,则该几何体的外接球的表面积为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/4f6fd8ec-0997-4763-9baa-df71a4e2e7bc.png?resizew=204)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/4f6fd8ec-0997-4763-9baa-df71a4e2e7bc.png?resizew=204)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
【推荐2】在四面体
中,
底面
,
,
,点
为三角形
的重心,若四面体
的外接球的表面积为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41dc595353570bdbfd6b403210f217f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c53bd865af8d453c8221021c4bbc93a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a07d806f971b0706f6369805138f42.png)
A.![]() | B.2 | C.![]() | D.![]() |
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