已知长方体的顶点都在球O表面上,长方体中从一个顶点出发的三条棱长分别为
,则球O的表面积是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680e9ef551b325387ab31dca1f893705.png)
更新时间:2023-06-16 23:52:57
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【推荐1】某多面体的三视图,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/2022/10/9/7e0c9034-62f8-4c75-a39e-8381703b9e2d.png?resizew=300)
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【推荐2】如图,矩形
中,
为
的中点,
,将
沿直线
翻折成
(
不在平面
内),连结
,
为
的中点,则在翻折过程中,下列说法中正确的是_________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/691334b0-bb75-440a-a744-71cf6f15cffa.png?resizew=195)
①
平面
;②存在某个位置,使得
;③当三棱锥
的体积最大时,三棱锥
的外接球的表面积是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/691334b0-bb75-440a-a744-71cf6f15cffa.png?resizew=195)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa6d64d90b17044cb17ff3061420c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770b4f16694b2bd79a1a93d776a82680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70eed72c64cc850a6d49e05580edad28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b47bffe27791c8a1cbb3180a480d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b47bffe27791c8a1cbb3180a480d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9609625b502348556ff8ba32deac8caa.png)
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【推荐1】《九章算术》把底面为直角三角形,且侧棱垂直于底面的三棱柱称为“堑堵”,把底面为矩形且有一侧棱垂直于底面的四棱锥称为“阳马”现有如图所示的“堑堵”
,其中
,当“阳马”即四棱锥
体积为
时,则“堑堵”即三棱柱
的外接球的表面积为 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81132a2b0c73194c5bfa9ff446e6560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd39dc736e2ebe01729e6661696f281c.png)
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![](https://img.xkw.com/dksih/QBM/2020/2/26/2407377191477248/2408204174581760/STEM/f5d81058-2dea-4544-936c-8964f0c9b3e8.png)
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【推荐2】鳖臑(biē nào)是我国古代对四个面均为直角三角形的三棱锥的称呼.已知三棱锥
是一个鳖臑,其中
,且
,则三棱锥
的外接球的表面积是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b050949b8fe7b275dd644c6356ea0.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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