Answer:
18
Step-by-step explanation:
33-15=18
V = Length x Width x Height = 288
If we call the width w
then length = 3w
And height = 288/(3w x w)
Assuming none of the material used overlaps the box will need 6 faces ( top, bottom, 2 ends and 2 sides)
Area of material = 2 x LW + 2 x HW + 2 x HL
= 2(3w x w + 288/(3w x w) x w + 288/(3w x w) x 3w)
= 2(3w^2 + 288/3w + 288/w)
= 2(3w^2 + 96/w + 288/w)
= 2(3w^2 + 384/w)
= 6w^2 + 768/w
Taking the derivative in terms of w
A’ = 12w - 768/w^2
A’ is zero when 12w = 768/w^2
w^3 = 768/12 = 64
w = cube root of 64 = 4
This makes the box with the minimum materials 12 x 4 x 6
So the length that uses the minimum material is 12 inches
1. 90 2. 8000 3. 500 4. 200,000
((5x5)/2)x2=50 square ft
(8x5)x2= 80 square ft
8x7= 56 square ft
50+80+56=186 square ft
D) 186 square ft