The optimum shape of such a box is half a cube. The corresponding cube will have a volume of 2×256 ft³ = 512 ft³ = (8 ft)³. Such a box has a square base that is 8 ft on a side. If the height is half that of the cube, it will be 4 ft.
The dimensions of your box will be 8 ft square by 4 ft high.
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If the base dimension is x ft, the area (quantity of material) is
... a = x² + 4x(256/x²)
... a = x² + 1024x⁻¹
Then the derivative of area with respect to x is
... a' = 2x -1024x⁻²
Setting this derivative to zero and solving for x gives the value of x for minimum area.
... 0 = 2x -1024/x²
... 512 = x³
... x = 8 . . . . . . . . same as above.
 
        
             
        
        
        
Answer:
3
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
x=11
Step-by-step explanation:
Explanation is in photo, hope this helps!
 
        
             
        
        
        
Answer:
I do not agree because Mario's claim is not general.
Step-by-step explanation:
Prime numbers: These are a set of numbers that are divisible by 1 and itself only. Examples are: 2, 3, 5, 7. 11 etc. 
And a  denominator is the divisor in a given fraction.
Considering the following fractions whose denominators are prime numbers:
 = 0.66666666...
 = 0.66666666...
 = 0.142857142
 = 0.142857142
 = 0.45454545...
 = 0.45454545...
 = 0.23076923
 = 0.23076923
 = 0.142857142
 = 0.142857142
It could be observed that Mario's claim is not a general principle which is applicable to all fractions with a prime denominator. Thus, I do not agree with his claim.