r=根號下4次方2a^2/3
h=2根號下a^2-r^2顯然滿足條件的圓柱被經(jīng)過圓心且平行于底面的平面平分為兩部分則圓柱底面積=πr²h=2√(a²-r²)V=πr²*2√(a²-r²)=4π√[(r²/2)²(a²-r²)]根據(jù)均值不等式(a²/3)³=[(r²/2+r²/2+a²-r²)/3]³≥(r²/2)²(a²-r²)當r²/2=a²-r²時取等號此時r=√6a/3，h=2√3a/3