Asked by Coc
A box with a square base and no top is to be built with a volume of 4000 in3. Find the dimensions of the box that requires the least amount of material. How much material is required at the minimum?
Answers
Answered by
Damon
V = x^2 h = 4000 so h = 4000/x^2
A = x^2 + 4 x h
A = x^2 + 4 x (4000/x^2)
A = x^2 + 16,000/x
dA/dx = 0 at max or min
0 = 2 x -16000/x^2
x^3 = 8000
x = 20
now do the rest
A = x^2 + 4 x h
A = x^2 + 4 x (4000/x^2)
A = x^2 + 16,000/x
dA/dx = 0 at max or min
0 = 2 x -16000/x^2
x^3 = 8000
x = 20
now do the rest
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