球面上有三点A，B，C，其中OA，OB，OC两两互相垂直（O为球心），且过A、B、C三点的截面圆的面积为 ，则
(1/2)\uff08\u6d59\u6c5f\u9ad8\u8003\uff09\u5982\u56fe\u2026\uff0c\u662f\u534a\u5f84\u4e3a1\u7684\u7403\u7684\u7403\u5fc3\uff0c\u70b9A\u3001B\u3001C\u5728\u7403\u9762\u4e0a\uff0cOA\u3001OB\u3001OC\u4e24\u4e24\u5782\u76f4\u3002\u3001\u5206\u522b\u662f\u5927...\u4f5cEG\u22a5OA\u4e8e\u70b9G\uff0c\u8fdeEG\u3001EF\u3001FG\uff0c\u5982\u56fe\uff0c
EG=1\u00d7sin\u03c0/4=\u221a2/2=FG\uff0c\u2220EGF= \u03c0/2
\u2234EF= \u221a EG^2+FG^2=1=OE=OF
\u2234\u2220EOF=\u03c0/3
\u2234E\u3001F\uff0c\u5728\u8be5\u7403\u9762\u4e0a\u7684\u7403\u9762\u8ddd\u79bb\u4e3a
\u03c0/3x1=\u03c0/3
\u7403\u8868\u9762\u79ef=4\u03c0R^2=4\u03c0,
\u5219\u7403\u534a\u5f84R=1\uff0c
\u56db\u9762\u4f53\u68f1OA=OB=OC=R=1\uff0c
\u56e0OA OB OC \u4e24\u4e24\u6240\u6210\u7684\u89d2\u90fd\u4e3a\u03c0\uff0f3\uff0c\u6545\u4ee5\u4e09\u89d2\u5f62ABC\u4e3a\u5e95\uff0c\u4e09\u4e2a\u4fa7\u68f1\u4e3a1\uff0c\u4e09\u4e2a\u4fa7\u9762\u4e09\u89d2\u5f62\u662f\u6b63\u4e09\u89d2\u5f62\uff0c\u5e95\u9762ABC\u4e5f\u662f\u6b63\u4e09\u89d2\u5f62\uff0c
\u4f5cOH\u22a5\u5e95\u9762ABC\uff0c\u5782\u8db3H\uff0c\u5219H\u662f\u5e95\u4e09\u89d2\u5f62\u7684\u5916\uff08\u91cd\u3001\u5185\u3001\u5782\uff09\u5fc3\uff0c\u8fde\u7ed3AH\uff0c\u4ea4\u5ef6\u957f\u4ea4BC\u4e8eD\uff0cAD=\u221a3/2\uff0cAH=2AD/3=\u221a3/3\uff0c
OH^2=OA^2-AH^2,
OH=\u221a6/3\uff0c
S\u25b3ABC=\uff08\u221a3/4\uff09*AB^2=\u221a3/4\uff0c
VO-ABC=S\u25b3ABC*OH/3=(\u221a3/4)* \u221a6/3/3=\u221a2/12.
\u56db\u9762\u4f53OABC\u7684\u4f53\u79ef\u662f\u221a2/12\u3002
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