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解题方法
1 . 鳖臑是我国古代对四个面均为直角三角形的三棱锥的称呼.如图,三棱锥
是一鳖臑,其中
,
,
,
,且高
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/21/2963077774426112/2964882593931264/STEM/cf2ffd26-da6d-41e6-93b8-e935f5b3de01.png?resizew=144)
(1)求三棱锥
的体积和表面积;
(2)求三棱锥
外接球体积和内切球的半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8915e8e775538d41debf1933102c6b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6834ac70927ae08d7d36a1922403c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f0459ed3af308dfbdaa5314d8ef327.png)
![](https://img.xkw.com/dksih/QBM/2022/4/21/2963077774426112/2964882593931264/STEM/cf2ffd26-da6d-41e6-93b8-e935f5b3de01.png?resizew=144)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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2022-04-24更新
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4卷引用:天津市第二十中学2022-2023学年高一下学期期中数学试题