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Integer sides of cuboid (Posted on 2021-02-17) Difficulty: 2 of 5
Determine a cuboid with minimal surface area, if its volume is strictly greater than 1000, and the lengths of its sides are integer numbers.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

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Solution computer solution | Comment 4 of 7 |
clc
fprintf('%s\n',"  edges   area volume")
minimum=9999999;
for a=1:20
    for b=a:20
        for c=b:20
            if a*b*c>1000
                A=2*(a*b+b*c+a*c);
                if A<=minimum
                    fprintf('%2d %2d %2d %5d %5d\n',a,b,c,A,a*b*c)
                    minimum=A;
                end
            end
        end
    end
end
                
finds the increasingly smaller areas:

  edges   area volume
 3 17 20   902  1020
 4 13 20   784  1040
 4 14 18   760  1008
 5 11 19   718  1045
 5 12 17   698  1020
 6  9 19   678  1026
 6 10 17   664  1020
 6 12 14   648  1008
 7  9 16   638  1008
 7 11 13   622  1001
 8  9 14   620  1008
 
The last is the best: 8 x 9 x 14 results in an area of 620, with a volume of 1008. 
                

  Posted by Charlie on 2021-02-17 10:05:26
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