Answer:
Dimensions will be
Length = 7.23 cm
Width = 7.23 cm
Height = 9.64 cm
Step-by-step explanation:
A closed box has length = l cm
width of the box = w cm
height of the box = h cm
Volume of the rectangular box = lwh
504 = lwh
Sides which involve length and width and height, cost = 3 cents per cm²
Top and bottom of the box costs = 4 cents per cm²
Cost of the sides = 3[2(l + w)h] = 6(l + w)h
= 3[2(l + w)h]
Cost of the top and the bottom = 4(2lw) = 8lw
Total cost of the box C = + 8lw
= + 8lw
To minimize the cost of the sides
---------(1)
-------(2)
Now place the value of w from equation (1) to equation (2)
l³ = 378
l = ∛378 = 7.23 cm
From equation (2)
w = 7.23 cm
As lwh = 504 cm³
(7.23)²h = 504
h = 9.64 cm