Question

已知一个底面为正方形的长方体容器,若下底面和四个侧面的面积和27,则当容器的容积最大时,底面边长的...

Answer 1

设底面边长x cm,高y cm (x>0,y>0)

x^2+4xy=27

y=-(1/4)×(x^2)+27/(4x)

V=X^2×y

=-(1/4)×x^3+(27/4)x

V'=-(3/4)x^2+(27/4)

令V'=0

-(3/4)x^2+(27/4)=0

x=±3 ∴x=3

答:底面边长为3