Answer:
A(x)=[tex]2*x^{2} +\frac{480}{x}[/tex]
Step-by-step explanation:
Length of the side of the square = [tex]x[/tex]
Therefore, Area of the square base = [tex]x^{2}[/tex]
Volume of a prism = Area of the base * Height of the prism
By making the Height of the prism the subject of the equation,
Height of the prism = [Volume of a prism / Area of the base]
Height of the prism = [tex]\frac{120}{x^{2} }[/tex] feet.
A prism with square base has 6 sides.
Area of the base and the top = [tex]2*x^{2}[/tex]
Area of the sides = [tex]4*x*\frac{120}{x^{2} }[/tex]
=[tex]\frac{480}{x}[/tex]
Surface area of the prism A(x)= Area of the base and the top + Area of the sides
=[tex]2*x^{2}[/tex] + [tex]\frac{480}{x}[/tex]
A(x)=[tex]2*x^{2} +\frac{480}{x}[/tex]
