Answer:
The volume of the medium box is 8 times the volume of the small box
The volume of the large box is 3.375 times the volume of the medium box
The volume of the large box is 27 times the volume of the small box
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
In this problem
1) The scale factor of the small box to the medium box is equal to
[tex]\frac{10}{5} =2[/tex]
The scale factor elevated to the cube is equal to
[tex]2^{3}=8[/tex]
therefore
The volume of the medium box is 8 times the volume of the small box
2) The scale factor of the medium box to the large box is equal to
[tex]\frac{15}{10} =1.5[/tex]
The scale factor elevated to the cube is equal to
[tex]1.5^{3}=3.375[/tex]
therefore
The volume of the large box is 3.375 times the volume of the medium box
3) The scale factor of the small box to the large box is equal to
[tex]\frac{15}{5} =3[/tex]
The scale factor elevated to the cube is equal to
[tex]3^{3}=27[/tex]
therefore
The volume of the large box is 27 times the volume of the small box
