Given:
Height of box = (x-2)
Volume of box = [tex](x^3-8)[/tex]
To find:
The expression for the base area.
Solution:
We know that,
Volume of a box(V) = Base area(B) × Height(h)
[tex]V=Bh[/tex]
[tex]\dfrac{V}{h}=B[/tex]
On substituting the given values, we get
[tex]B=\dfrac{x^3-8}{x-2}[/tex]
[tex]B=\dfrac{x^3-2^3}{x-2}[/tex]
[tex]B=\dfrac{(x-2)(x^2+2x+2^2)}{x-2}[/tex] [tex][\because a^3-b^3=(a-b)(a^2+ab+b^2)][/tex]
[tex]B=x^2+2x+4[/tex]
So, the base area is [tex]x^2+2x+4[/tex].
Therefore, the correct option is B.
