Question

A small box in the shape of a cube for packaging has a volume of 64 cubic inches.

Answer 1

1. The volume of a medium box is 512 cubic inches.
2. The ratio of the sides of the small box to the medium box is 1:2.
3. The ratio of the area of the small box to the medium box is 1:4.
4. The ratio of the volume of the small box to the medium box is 1:8.

What are the ratio of the small box to the medium box?

The first step is to determine the side lengths of the small box.

Side length = ∛64 = 4 in

Side lengths of the medium boxes = 4 x 2 = 8 inches

Volume of the medium box = 8³ = 256 cubic inches

The ratio of the sides of the small box to the medium box = 4 : 8 = 1:2.

The ratio of the area of the small box to the medium box= (4 x 4) : (8 x 8) =  1:4.

The ratio of the volume of the small box to the medium box = 4³ : 8³ = 1 : 8.

To learn more about the volume of a cuboid, please check: brainly.com/question/26406747