Question

What is the possible expression for the dimension of the cuboid whose volume is given below?
Volume : $3{x^2} - 12x$
(A) \[4 \times x \times (x - 4)\]
(B) \[3 \times x \times (x - 4)\]
(C) \[4 \times x \times (x + 4)\]
(D) \[3 \times x \times (x + 4)\]

Answer 1

Hint: Talking about cuboids, a cuboid is a very common shape in our environment all around. All of us see rectangular boxes, bricks, books around us. These are referred to as cuboids. We need to mention that a cuboid is a closed or bounded figure, which has a definite height, width and length.

Complete step-by-step solution:
In this particular problem we the volume of the cuboid is already given. We are to find out the expression of the given cuboid. So, we will find out the possible values of the height, width and length of the cuboid.
In this case, we should know that the volume of a cuboid is generally denoted by $V$and is defined by $V = w \times l \times h$ where $w = $ width, $l = $ length and $h = $ height of the cuboid. In simple words, the volume of the cuboid is the product of the width, length and the height of the cuboid.
Here the volume, $V = 3{x^2} - 12x$ .
If we observe closely, we see that we can take $3$ as a common product from the above expression. Then, taking $3$ as common, we get $V = 3 \times ({x^2} - 4x)$. Again, we see that $x$ can be taken as a common product from the expression $({x^2} - 4x)$. Therefore, taking $x$ as common, we have $V = 3 \times x \times (x - 4)$ which is similar as option no. (B).
Therefore, the possible values of the width, height and length of the given cuboid is $3,x,(x - 4)$.
Thus option (B) is correct.

Note: The exact definition of a cuboid is: A cuboid is a three dimensional closed and bounded figure which has six quadrilateral faces. Note that, a cuboid has $6$ faces, $12$ edges and $8$ vertices. The formula to determine the surface area of a cuboid is given by, Surface Area$ = 2\left( {lw + hl + wh} \right)$ where w, h and l have the same meaning as discussed before.