SOLUTION: A box has rectangular top, bottom, and sides. The top and bottom are square. The volume must be 8 cubic meters. Express the total surface area A of the box in terms of the height h

Algebra ->  Surface-area -> SOLUTION: A box has rectangular top, bottom, and sides. The top and bottom are square. The volume must be 8 cubic meters. Express the total surface area A of the box in terms of the height h      Log On


   

Question 392572: A box has rectangular top, bottom, and sides. The top and bottom are square. The volume must be 8 cubic meters. Express the total surface area A of the box in terms of the height h (in meters) of the box.
Answer by mananth(16946) About Me  (Show Source):
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A box has rectangular top, bottom, and sides. The top and bottom are square. The volume must be 8 cubic meters. Express the total surface area A of the box in terms of the height h (in meters) of the box.
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Volume V = L*W*H
8= L*W*H
the top and bottom are square
8 = l^2*H
8/h = l^2= area of top & bottom face of the box
..
l= sqrt(8/H)
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Surface area of the closed box = 2(LW+WH+LH)
A=+2%2A%28sqrt%288%2FH%29%2Asqrt%288%2FH%29+%2Bsqrt%288%2FH%29%2AH+%2Bsqrt%288%2FH%29%2AH%29
A=2%2A%28%288%2FH%29%2Bsqrt%288H%29%2Bsqrt%288H%29%29
...
A=2%2A%28%288%2FH%29%2B2sqrt%288H%29%29
A=2%2A%28%288%2FH%29%2B4sqrt%282H%29%29
A=+2%2A4%28%282%2FH%29%2Bsqrt%282H%29%29
A=+8%2A%28%282%2FH%29%2Bsqrt%282H%29%29
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m.ananth@hotmail.ca