题目内容
将边长为2的正
沿
边上的高
折成直二面角
,则三棱锥
的外接球的表面积为 .
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5
π/6
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解:根据题意可知三棱锥B-ACD的三条侧棱BD、DC、DA两两互相垂直,
所以它的外接球就是它扩展为长方体的外接球,所以求出长方体的对角线的长为: 1+1 +(
)2 =
,所以球的直径是 5 ,半径为
/ 2 ,所以球的体积为:4πr3 /3 ="5"
π/ 6.故答案为:5
π/6
所以它的外接球就是它扩展为长方体的外接球,所以求出长方体的对角线的长为: 1+1 +(
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