SOLUTION: A box has rectangular top, bottom, and sides. The top and bottom are square. The volume must be 6 cubic meters. Express the total surface area A of the box in terms of the height h

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Question 254949: A box has rectangular top, bottom, and sides. The top and bottom are square. The volume must be 6 cubic meters. Express the total surface area A of the box in terms of the height h (in meters) of the box.
A(h)= _____ m^2
Found 2 solutions by CharlesG2, palanisamy:
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
A box has rectangular top, bottom, and sides. The top and bottom are square. The volume must be 6 cubic meters. Express the total surface area A of the box in terms of the height h (in meters) of the box.
A(h)= ______ m^2
a rectangular box has 6 sides
top and bottom are squares so they have equal areas
V=s^2*h=6
s^2=6/h
s=sqrt(6/h)
area (A) of sides (will use w): 2*s^2 + 4*s*h
(2*6)/h + 4*h*sqrt(6/h)
12/h + 4*h*6^(1/2)*h^(-1/2)
12h + 4*6^(1/2)*h^2*h^(-1/2)
12h + 4*sqrt(6)*h^(3/2)
12h + 9.7980*h^(3/2) rounded to 4 places

Answer by palanisamy(496) About Me  (Show Source):
You can put this solution on YOUR website!
A box has rectangular top, bottom, and sides. The top and bottom are square.
Let a be the side of the square base and h be the height.
Its volume a^2h = 6
a^2 =6/h
Total surface area A = 6a^2
A = 6(6/h)
A = 36/h square meters