Originally Posted by
ilsj6 I understand what you wrote and that is how I solved it, initially. However, my answer just didn't seem right because that is what you would get if you solved it without Calculus. My work:
V = L^2(h)
450 = L^2(h)
h = 450/(L^2)
SA = (2L^2) + (1800L/(L^2))
I took the derivative:
SA' = 4L - (1800/(L^2))
Set it equal to zero and solved for "L:"
0 = 4L - (1800/(L^2))
-4L = - (1800/(L^2))
-4L^3 = -1800
L^3 = 450
L = 7.66
From here, I plugged it back into the volume formula to solve for "h:"
450 = 58.6756h
h = 7.669 = 7.67
Basically, my height, width, and length would approximately be 7.66 inches to minimize the Surface Area.
Is this correct?