在正三棱锥P—ABC中,侧棱PC⊥侧面PAB,侧棱PC=2,则此正三棱锥的外

在正三棱锥P—ABC中,侧棱PC⊥侧面PAB,侧棱PC=2,则此正三棱锥的外接球的表面积为________________.

答案

36π

解:∵三棱锥P—ABC为正三棱锥,PC⊥面PAB,

∴PC⊥PA,PC⊥PB且PA⊥PB.又PC=2

∴外接球的直径为2·=6,半径为3.

∴S=4π×32=36π.

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