Answer:
The dimensions that minimize the amount of cardboard used is
x = 31 cm , y = 34 cm & Z = 15.54 cm
Step-by-step explanation:
Volume of the cardboard = 16,384 
The function that represents the area of the cardboard without a lid is given by
------ (1)
Volume of the cardboard with sides x, y & z is


Put this value of z in equation (1) we get


Differentiate above equation with respect to x & y we get


Take 

------ (2)
------- (3)
By solving equation (2) & (3) we get

x = 31 cm
From equation 2

y = 32768 (
)
y = 34 cm


Z = 15.54 cm
Thus the dimensions that minimize the amount of cardboard used is
x = 31 cm , y = 34 cm & Z = 15.54 cm