document.write( "Question 1155310: A box with a square top and bottom is to be made to contain a volume of 64 cubic inches. What should be the dimensions of the box if its surface area is to be minimum? What is this minimum surface area? \n" ); document.write( "
Algebra.Com's Answer #777898 by Cromlix(4381)\"\" \"About 
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Hi,
\n" ); document.write( "Taking the measurements of the length and breadth of the base and top of the box = x
\n" ); document.write( "Taking it to be a closed box (Closed top and bottom)
\n" ); document.write( "Volume = x^2 h (h being height)
\n" ); document.write( "Volume = 64 ins^3
\n" ); document.write( "x^2 h = 64
\n" ); document.write( "Therefore h = 64/x^2
\n" ); document.write( "Surface area = 2x^2 (top and bottom)+ 4xh (4 sides)
\n" ); document.write( "Surface Area = 2x^2 + 4xh
\n" ); document.write( "(Removing the h) by multiplying 4xh by 64/x^2 (h)
\n" ); document.write( "4xh * 64/x^2 ( * means times)
\n" ); document.write( "= 256/x
\n" ); document.write( "Surface Area = 2x^2 + 256/x
\n" ); document.write( "S.A.(x) = 2x^2 + 256x^-1
\n" ); document.write( "S.A.'(x)= 4x - 256x^-2
\n" ); document.write( "S.A.' (x) = 4x - 256/x^2
\n" ); document.write( "S.A.' (x) = 0
\n" ); document.write( " 4x - 256/x^2 = 0
\n" ); document.write( " - 256/x^2 = - 4x (Multiply both sides by -1)
\n" ); document.write( " 256/x^2 = 4x (Cross multiply)
\n" ); document.write( " 256 = 4x^3
\n" ); document.write( " 4x^3 = 256
\n" ); document.write( " x^3 = 64
\n" ); document.write( " x = cube root of 64
\n" ); document.write( " x = 4
\n" ); document.write( "Nature Table shows x = 4 to be a minimum value
\n" ); document.write( "Therefore Length = Breadth = 4 ins
\n" ); document.write( "Height = 64/x^2 = 64/16 = 4 ins.
\n" ); document.write( "Hope this helps :-)
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