江西省2023-2024学年第一学期九年级期中质量检测数学.考卷答案试卷答案,我们目前收集并整理关于江西省2023-2024学年第一学期九年级期中质量检测数学.考卷答案得系列试题及其答案，更多试题答案请关注微信公众号：考不凡/直接访问www.kaobufan.com(考不凡)
江西省2023-2024学年第一学期九年级期中质量检测数学.考卷答案试卷答案
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分析三棱锥A-BCD中，侧棱AB、AC、AD两两相等且相互垂直，补成正方体，两者的外接球是同一个，正方体的对角线就是球的直径，由此能求出侧棱长．
解答解：三棱锥A-BCD中，侧棱AB、AC、AD两两相等且相互垂直，补成正方体，
两者的外接球是同一个，正方体的对角线就是球的直径，
设侧棱的长为a，外接球的半径为R，
∵外接球的表面积S=4π，∴4πR2=4π，
∴R=1，
∵正方体的对角线就是球的直径，
∴$\sqrt{3}$a=1，解得a=$\frac{\sqrt{3}}{3}$．
∴侧棱长为$\frac{\sqrt{3}}{3}$．
点评本题考查棱锥侧棱长的求法，是中题，解题时要认真审题，注意构造法的合理运用．
