The volume of a box is the amount of space in it
The maximum capacity of box B is 14400
The dimensions of box A are:
[tex]\mathbf{Height = 567}[/tex]
[tex]\mathbf{Width = 678}[/tex]
[tex]\mathbf{Length = 789}[/tex]
The dimensions of box B are:
[tex]\mathbf{Height = 3 \times 567 = 1701}[/tex]
[tex]\mathbf{Width = 4 \times 678 = 2712}[/tex]
[tex]\mathbf{Length = 289}[/tex]
Calculate the volumes of both boxes
[tex]\mathbf{V_A = 567 \times 678 \times 789}[/tex]
[tex]\mathbf{V_A = 303312114}[/tex]
[tex]\mathbf{V_B = 1701 \times 2712 \times 789}[/tex]
[tex]\mathbf{V_B = 3639745368}[/tex]
Express as ratios
[tex]\mathbf{VA: V_B = 303312114 : 3639745368}[/tex]
Substitute 1200 for VA (the capacity of box A)
[tex]\mathbf{1200 : V_B = 303312114 : 3639745368}[/tex]
Express as fractions
[tex]\mathbf{\frac{V_B }{1200}= \frac{ 3639745368}{303312114}}[/tex]
[tex]\mathbf{\frac{V_B }{1200}= 12}[/tex]
Make Vb the subject
[tex]\mathbf{V_B = 12 \times 1200}[/tex]
[tex]\mathbf{V_B = 14400}[/tex]
Hence, the maximum capacity of box B is 14400
Read more about volumes at:
https://brainly.com/question/23952628
