Asked by TayB
A box with a square base and open top must have a volume of 4,000 cm^3. Find the dimensions of the box that minimize the amount of material used.
sides of base cm
height cm
sides of base cm
height cm
Answers
Answered by
TayB
For sides of base I got 20cm and for height I got 10 cm? Anybody agree or disagree with me?
Answered by
Steve
the volume
v = x^2 z = 4000, so z = 4000/x^2
the area is
a = x^2 + 4xz = x^2 + 16000/x
da/dx = 2x - 16000/x^2
da/dx=0 when
2x - 16000/x^2 = 0
x^3 = 8000
x = 20
So the box is 20x20x10 cm
v = x^2 z = 4000, so z = 4000/x^2
the area is
a = x^2 + 4xz = x^2 + 16000/x
da/dx = 2x - 16000/x^2
da/dx=0 when
2x - 16000/x^2 = 0
x^3 = 8000
x = 20
So the box is 20x20x10 cm
Answered by
TayB
Same as what I got
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