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.
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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
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l= sqrt(8/H)
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Surface area of the closed box = 2(LW+WH+LH)
{{{A= 2*(sqrt(8/H)*sqrt(8/H) +sqrt(8/H)*H +sqrt(8/H)*H)}}}
{{{A=2*((8/H)+sqrt(8H)+sqrt(8H))}}}
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{{{A=2*((8/H)+2sqrt(8H))}}}
{{{A=2*((8/H)+4sqrt(2H))}}}
{{{A= 2*4((2/H)+sqrt(2H))}}}
{{{A= 8*((2/H)+sqrt(2H))}}}
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