设高为h
V=(3^0.5/4)*h*a^2
所以h=(4*3^0.5)V/3a^2
表面积S=3ah+2(3^0.5/4)*a^2
=(4*3^0.5)V/a+3^0.5*a^2/2
=(2*3^0.5)V/a+(2*3^0.5)V/a+3^0.5*a^2/2
S最小时,(2*3^0.5)V/a=3^0.5*a^2/2
a=（4V）^(1/3)
就是4V开三次根号