已知半球内有一个内接正方体,正方体的一个面在半球的底面圆内,若正方体的棱长为
,则半球的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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更新时间:2022-01-08 21:58:34
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【推荐1】已知球
的半径为
,
,
,
三点在球
的球面上,球心
到平面
的距离为
,
,
,则球
的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2a611e62fe0d6c6519a16b25423cec.png)
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【推荐2】如图,正四棱锥
底面的四个顶点
在球
的同一个大圆上,点
在球面上.若
,则球
的体积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/5bffa68a-00fd-49a9-8428-1ae4c4cfe68a.png?resizew=140)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad9860eaa4bf85ef09921ea377176c.png)
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【推荐1】已知某棱长为
的正四面体的各条棱都与同一球面相切,则该球与此正四面体的体积之比为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
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解题方法
【推荐2】三棱锥
中,
,
,
为等边三角形,二面角
的余弦值为
,且三棱锥的体积为
.则三棱锥外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
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