在封闭的直三棱柱ABC-A1B1C1内有一个体积为V的球，若AB⊥BC，AB=6，BC=8，AA1=3，则V的最大值是()
A.[img src="https://img.haodaxue.net/uploadimg/ico/2020/0606/1591435186290359.png" />
B.[img src="https://img.haodaxue.net/uploadimg/ico/2020/0606/1591435197993464.png" />
C.[img src="https://img.haodaxue.net/uploadimg/ico/2020/0606/1591435208903119.png" />
D.[img src="https://img.haodaxue.net/uploadimg/ico/2020/0606/1591435219963658.png" />
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正确答案： B 答案分析： 由题意知，当球为直三棱柱的内接球时，体积最大，选取过球心且平行于直三棱柱底面的截面，如图所示，则由切线长定理可知，内接圆的半径为 2，[img src="https://img.haodaxue.net/uploadimg/image/20200606/20200606172102_31168.png" alt="" />
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