EXPLANATION
The new cereal box has the form of a cube.
The volume of the cube is given by the expression a^3
Where a is the side of the cube. This is equal to the volume of the original box.
[tex]a^3=12*8*2=192_{\text{ }}in^3[/tex]
Isolating the value of a:
[tex]a=\sqrt[3]{192}[/tex]
Computing the cubic root:
[tex]a=5.7689[/tex]
Then, the surface area of the box is the following:
[tex]Surface=6a^2[/tex]
Plugging in the values:
[tex]Surface=6(5.77)^2=199.75in^2[/tex]
This area is more than the surface of the original box.
In conclusion, the manufacturing cost of the new cereal box will be more.
