Question

How do you find the volume of the box given the dimensions are: 3x + 1, 2x – 1 and x + 2?

Answer 1

Hint:In the given question, we have been asked to find the volume of the box. First, we observe that the dimensions given are i.e. length, breadth and height are of different measures thus the given box is of cuboid shape. In order to find the volume, it is equal to the multiplication of length, breadth and the height.

Complete step by step answer:
We have given that,
A box with the dimensions: $3x + 1, 2x – 1\,and\,x + 2$.
The formula used for the volume of a box is given by;
Volume of a box = \[length\times breadth\times height\].
Here,
Length = $3x + 1$
Breadth = $2x – 1$
Height = $x + 2$
Therefore,
Volume of a box =\[\left( 3x+1 \right)\times \left( 2x-1 \right)\times \left( x+2 \right)\].
Expanding the above using the distributive property of multiplication;
Volume of a box =\[\left[ \left( 3x \right)\left( 2x-1 \right)+1\left( 2x-1 \right) \right]\times \left( x+2 \right)\].
Simplifying the brackets; we obtained
Volume of a box =\[\left[ 6{{x}^{2}}-3x+2x-1 \right]\times \left( x+2 \right)\].
Volume of a box =\[\left[ 6{{x}^{2}}-x-1 \right]\times \left( x+2 \right)\].
Expanding the above using the distributive property of multiplication,
Volume of a box =\[\left[ 6{{x}^{2}}\left( x+2 \right)-x\left( x+2 \right)-1\left( x+2 \right) \right]\].
Simplifying the brackets, we get
Volume of a box =\[\left[ 6{{x}^{3}}+12{{x}^{2}}-{{x}^{2}}-2x-x-2 \right]\].
Volume of a box =\[6{{x}^{3}}+12{{x}^{2}}-{{x}^{2}}-3x-2\].

Therefore the volume of a given box is \[6{{x}^{3}}+12{{x}^{2}}-{{x}^{2}}-3x-2\].

Note:In order to find the volume of the given box, students should remember the formula of finding the volume of a box. We know that the volume of any figure is the multiplication of the height with the area of the base that is multiplication of length and breadth. If all the dimensions of a box given are of equal measure then the formula is the multiplication of given sides three times by itself i.e. side to the power of 3.