A cardboard box without a lid is to have a volume of 23,328 cm3. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.)

x,y,z=36cm, 36cm, 18cm

Step-by-step explanation:

Volume of the Cardboard =

The dimensions of the box are x, y and z.

Volume of a Cuboid = xyz.

Since the top is open, there is only one 'xy' side.

Surface Area, f(x,y,z)= xy+2yz+2xz

We take the first derivative of f(x,y)

Equate the derivatives to zero and solve for x and y respectively.

Substituting x into y and vice versa

Recall:

x,y,z=36cm, 36cm, 18cm

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