SOLUTION: Casey and Chris want to design an open topped box having a square base and a surface area of 108 square inches. What dimensions would the box of greatest volume have?

Question 337440: Casey and Chris want to design an open topped box having a square base and a surface area of 108 square inches. What dimensions would the box of greatest volume have?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
square box top open
so the surface area will be 5 times the area of each face.
since the box is open at top only 5 sides.
let lebgth be x
area of 1 face of the box = x^2
5x^2 = total area.
5x^2=108
x^2= 108/5
x^2= 21.6
take sqrt
x= sqrt 21.6
4.65 inches is the side of the box
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