Given:
Each side of the cube shaped box = [tex]2x-3[/tex]
To find the surface area of the box and the volume of the box.
Formula
If the each side of cube is a,
[tex](a-b)^{3}=a^{3}-3a^{2} b+3a^{2} b-b^{3}[/tex]
[tex](a-b)^{2}=a^{2}+b^{2}-2ab[/tex]
Now,
Putting [tex]a =[/tex] [tex]2x-3[/tex] we get,
The surface area, [tex]SA =6(2x-3)^{2}[/tex] sq unit
[tex]SA = 6(4x^{2}-12x+9)[/tex] sq unit
[tex]SA = 24x^{2} -72x+54[/tex] sq unit
And,
The volume, [tex]V = (2x-3)^{3}[/tex] cube unit
[tex]V = 8x^{3}- 36x^{2} +54x-27[/tex] cube unit
Hence,
The surface area of the box is [tex]24x^{2} -72x+54[/tex] sq unit and
The volume of the box is [tex]8x^{3} -36x^{2} +54x-27[/tex] cube unit.
