Answer : The volume of box B is [tex]64m^3[/tex]
Step-by-step explanation :
Given :
Volume of box A = 512 cubic meter
Let us assumed that the box A and box B are cubes and the dimensions of cube are same i.e, 'a'.
Volume of box A = V = [tex]a\times a\times a=a^3[/tex]
As per question,
When dimensions of box A divided by 2 then the volume of box B will be:
Volume of box A = V' = [tex]\frac{a}{2}\times \frac{a}{2}\times \frac{a}{2}=\frac{a^3}{8}[/tex]
As the box B is similar to box A. So, the volume of box B will be:
Volume of box B = V' = [tex]\frac{a^3}{8}[/tex]
[tex]V'=\frac{a^3}{8}=\frac{V}{8}[/tex]
[tex]V'=\frac{512m^3}{8}=64m^3[/tex]
Therefore, the volume of box B is [tex]64m^3[/tex]
