Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box.) (x, y, z)

Dimensions of side with minimum surface area is 12 cm

Given that;

Volume of box = 1728 cubic centimeter

Find:

Dimensions of side with minimum surface area

Computation:

Dimensions of side with minimum surface area is with cube

So,

Assume; Side = a

Volume of box = side³

Side³ = 1728

Side = ∛1728

Side = 12 cm

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The dimensions of the box are 12 cm , 12 cm , 12 cm

Step-by-step explanation:

Let x , y and z be the dimensions of box

Volume of box =xyz=1728

Surface area of box =

Let

To get minimal surface area

and

----1

Using 1

x=0 and

Side can never be 0

So,

x=12

y=12

z=12

The dimensions of the box are 12 cm , 12 cm , 12 cm

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