正四面体SABC的棱长为a,求他的内切球,外切球的体积
\u68f1\u957f\u4e3aa\u7684\u6b63\u56db\u9762\u4f53\u7684\u5185\u5207\u7403\u4e0e\u5916\u63a5\u7403\u7684\u4f53\u79ef\u6bd4\u662f\u591a\u5c111/(3 *\u6839\u53f73)
\u89e3\u7b54\uff1a\u89e3\uff1a\u8bbe\u6b63\u56db\u9762\u4f53\u7684\u9762BCD\u548c\u9762ACD\u7684\u4e2d\u5fc3\u5206\u522b\u4e3aO1\uff0cO2\uff0c\u8fde\u7ed3AO2\u4e0eBO1\u5e76\u5ef6\u957f\uff0c\u5fc5\u4ea4\u4e8eCD\u7684\u4e2d\u70b9E\uff0c\u53c8BE=32a\uff0cO2E=36a\uff0c\u8fde\u63a5BO2\uff0c\u5728Rt\u25b3BO2E\u4e2d\uff0cBO2=63\uff0c\u8fde\u7ed3AO1\u4e0eBO2\u4ea4\u4e8eO3\uff0c\u7531Rt\u25b3AO2O3\u224cRt\u25b3BO1O2\uff0c\u2234O3O2=O3O1\uff0cO3A=O3B\uff0c\u540c\u7406\u53ef\u8bc1O3C=O3D=O3A\uff0cO3\u5230\u53e6\u4e8c\u9762\u7684\u8ddd\u79bb\u4e5f\u7b49O3O1\uff0c\u2234O3\u4e3a\u56db\u9762\u4f53\u5916\u63a5\u7403\u4e0e\u5185\u63a5\u7403\u7684\u7403\u5fc3\uff0c\u7531\u25b3BO1O3\u223d\u25b3BO2E\uff0c\u2234O1O3=612a\uff0c\u2234R\u5916=64a\uff0cS\u5916=32\u03c0a2\uff0cr\u5185=612a\uff0cS\u5185=16\u03c0a2\uff0e
外接球体积V=√6／8πa³内切球体积V=√6／216πa³
这个最好自己推一遍吧，然后就容易记了
绛旓細澶栨帴鐞冧綋绉疺=鈭6锛8蟺a³鍐呭垏鐞冧綋绉疺=鈭6锛216蟺a³
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