SOLUTION: A parcel delivery service has contracted you to design an open box with square base of length x cm and height y cm and a volume of 3600 cubic cm. Find the total surface area in ter

Click here to see ALL problems on Surface-area

Question 863807: A parcel delivery service has contracted you to design an open box with square base of length x cm and height y cm and a volume of 3600 cubic cm. Find the total surface area in terms of x and y. Also determine the dimensions for minimum surface area. (Round your answers correct to two decimal places if needed.) I know the formula to solve this is S=x^2+4xy but I don't know where to start. Can someone break this down step by step so I can understand.
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
There are two equations to consider
S = x^2 + 4xy
V = x^2*y and V = 3600
y = V/x^2
S = (x^2 +4xy)
S = (x^2 +4*x*V/x^2)
dS/dx = 2x -4V/x^2
now set derivative to 0 for min surface area
2x = 4V/x^2
x^3 = 2V
x = (2V)^(1/3) = (7200)^1/3 = 19.31 cm
y = 3600 / x^2 = 3600 / 19.31^2 = 9.65 cm