Question

2. You have a set of three similar gift boxes. Each box is a rectangular prism. The large box has 15-cm base edges. The medium box has 10-cm base edges. The small box has 5-cm base edges. How does the volume of each box compare to every other box?

PLEASE HELP!!!!

Answer 1

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

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

`(10)/(5) =2`

The scale factor elevated to the cube is equal to

`2^(3)=8`

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

`(15)/(10) =1.5`

The scale factor elevated to the cube is equal to

`1.5^(3)=3.375`

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

`(15)/(5) =3`

The scale factor elevated to the cube is equal to

`3^(3)=27`

therefore

The volume of the large box is 27 times the volume of the small box