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kirill115 [55]
2 years ago
7

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 l

east amount of material. how much material is required at the minimum?
Mathematics
1 answer:
vekshin12 years ago
6 0

Let the length of the square base be x inches .

And the height of the box be y inch .

Volume = x*x*y

4000 = x *x *y

y = \frac{4000}{x^2}

S = x*x + 2xy + 2 x y

S = x^2 + 4 xy

S = x^2+ 4x* \frac{4000}{x^2}

S = x^2 + \frac{16000}{x}

S ' = 2x - \frac{16000}{x^2}

S ' =0

2x - \frac{16000}{x^2}=0

2x^3 - 16000 = 0

x^3 = 8000

x = 20

y =  \frac{4000}{20^2} = \frac{4000}{400} = 10

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