Question

7) The height of a box is represented by the expression
(x.- 2) centimeters. The volume of the same box is
represented by the expression (x3 - 8 ) cubic centimeters.
Which expression below represents the area of the base of the
box?
A. x2 – 2x + 4
B. x2 + 2x + 4
C. X? + 6x - 4
D. x2 - 6x + 4

Answer 1

Given:

Height of box = (x-2)

Volume of box = $(x^3-8)$

To find:

The expression for the base area.

Solution:

We know that,

Volume of a box(V) = Base area(B) × Height(h)

$V=Bh$

$\dfrac{V}{h}=B$

On substituting the given values, we get

$B=\dfrac{x^3-8}{x-2}$

$B=\dfrac{x^3-2^3}{x-2}$

$B=\dfrac{(x-2)(x^2+2x+2^2)}{x-2}$   $[\because a^3-b^3=(a-b)(a^2+ab+b^2)]$

$B=x^2+2x+4$

So, the base area is $x^2+2x+4$.

Therefore, the correct option is B.