Find the dimensions of the box with volume 8000 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box.)

Step-by-step explanation:

Given

Required

Determine the dimensions that minimizes the surface area.

Surface area of a box is;

Volume of a box is:

Make z the subject

Substitute 8000 for V

Substitute 1000/xy for z in

Expand:

Differentiate S w.r.t x

Differentiate S w.r.t y

Equate both differentiation to 0

Multiply through by

Divide through by 2

-- (1)

Multiply through by x^2

Divide through by 2

--- (2)

Divide (1) by (2)

Substitute y for x in (1)

Take cube roots

Hence;

Recall that:

Hence, the dimension of the box that minimizes the surface area of the box is:

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!