Answer:
Step-by-step explanation:
Base area =[tex]x^2[/tex]
side area=[tex]h*x[/tex]
Volume=[tex]x^2*h[/tex]=14
Surface area =[tex]4hx+2x^2[/tex]
upon substituting [tex]h=14/x^2[/tex]
surface area = [tex]4*\frac{14}{x^2}*x+2x^2[/tex]
upon differentiating and solving we get f"([tex]\sqrt[3]{14\\}[/tex]) >0 proves that this point is of minima
hence, dimensions are
[tex]x=\sqrt[3]{14}[/tex] ,h=[tex]\sqrt[3]{14}[/tex]
