设球半径R,上柱半径r2,下注半径r1r1²=R²-h²r2²=R²-(2h)²两圆柱体积之和V=f(h)=πr1²h+πr2²h=πh(2R²-5h²)=π(2R²h-5h³)f'=π(2R²-15h²)h=R√(2/15)时,f'=0,体积最大Vmax=π(2R³√(2/15)-5R³.2/15.√(2/15))=πR³(2-2/3)√(2/15)=(4/3)πR³√(2/15)
秋浦歌(李白)