5、高 h = 16π/r^2π = 16/r^2表面积S = 2 * πr^2 + 2πrh =2 * πr^2 +2πr * 16/r^2 =2π(r^2 + 8/r + 8/r )由均值不等式,r^2 + 8/r + 8/r≥ 3³√(r^2 * 8/r * 8/r ) =3³√64 = 12;当r^2 = 8/r,即r = 2时,r^2 + 8/r + 8/r有最小值 12;即r = 2,h = 16/2^2 = 4时,所用材料最省 。6,设小正方形的边长为x;容积V = ( 6 - 2x )x = -2[ x^2 - 3x + (3/2)^2 ] + 2(3/2)^2 = -2( x - 3/2 )^2 + 9/2故当x = 3/2时,V有最大值 9/2,盒子容积最大 。