Answer:
[tex]\dfrac{2s^3+136}{s}[/tex]
Step-by-step explanation:
Let the side length of the square base =s feet
Let the height of the box = h
Given that the volume of the box = [tex]34$ ft^3[/tex]
Volume of the box =[tex]s^2h[/tex]
Then:
[tex]s^2h=34$ ft^3\\$Divide both sides by s^2\\h=\dfrac{34}{s^2}[/tex]
Surface Area of a Rectangular Prism =2(lb+bh+lh)
Since we have a square base, l=b=s feet
Therefore:
Surface Area of our closed box[tex]= 2(s^2+sh+sh)[/tex]
[tex]S$urface Area= 2s^2+4sh\\Recall: h=\dfrac{34}{s^2}\\$Surface Area= 2s^2+4s\left(\dfrac{34}{s^2}\right)\\=2s^2+\dfrac{136}{s}\\$Surface Area in terms of length only=\dfrac{2s^3+136}{s}[/tex]
