Question

The dimensions of a box are x, 2x, and 3x. Each dimension is decreased by 2. Calculate the volume of the box.

Answer 1

Question :

The dimensions of a box are x, 2x, and 3x. Each dimension is decreased by 2. Calculate the volume of the box.

Solution :

Dimensions of a box

• Length = x
• Breadth =2x
• Height=3x

Now each dimension is decreased by 2.

New Dimensions of a box :

• Length = x-2
• Breadth =2x-2
• Height=3x-2

Diagram : Box

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\put(8,5.5){x-2m}\put(4,6.3){2x-2 m}\put(11.2,7.5){3x-2 m}\end{picture}$

Volume of the box

= Length ×Breadth ×Height

$\sf{=(x-2)(2x-2)(3x-2)}$

$\sf{=(2x^2-2x-4x+4)(3x-2)}$

$\sf{=(2x^2-6x+4)(3x-2)}$

$\sf{=6x^3-18x^2+12x-4x^2+12x-8}$

$\sf{=6x^3-22x^2+24x-8}$

Hence ,The volume of box is $\sf{6x^3-22x^2+24x-8}$

Answer 2

Answer:

Dimensions of a box

Length = x

Breadth =2x

Height=3x

Now each dimension is decreased by 2.

New Dimensions of a box :

Length = x-2

Breadth =2x-2

Height=3x-2

Diagram : Box

\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\put(8,5.5){x-2m}\put(4,6.3){2x-2 m}\put(11.2,7.5){3x-2 m}\end{picture}

Volume of the box

= Length ×Breadth ×Height

\sf{=(x-2)(2x-2)(3x-2)}=(x−2)(2x−2)(3x−2)

\sf{=(2x^2-2x-4x+4)(3x-2)}=(2x

2

−2x−4x+4)(3x−2)

\sf{=(2x^2-6x+4)(3x-2)}=(2x

2

−6x+4)(3x−2)

\sf{=6x^3-18x^2+12x-4x^2+12x-8}=6x

3

−18x

2

+12x−4x

2

+12x−8

\sf{=6x^3-22x^2+24x-8}=6x

3

−22x

2

+24x−8

Hence ,The volume of box is \sf{6x^3-22x^2+24x-8}6x

3

−22x

2

+24x−8