The ratio of the side lengths for two similar cubes is 2: 5. determine the ratios for each of the following. show your work or explain how you got your awsners.

a. the perimeter of once face of the smaller cube compared to the perimeter of one face of the larger cube.

b. the total surface area of the smaller cube compared to the total surface area of the larger cube.

c. the volume of the smaller cube compared to the volume of the larger cube.

Part A) The ratio of the perimeter of once face of the smaller cube compared to the perimeter of one face of the larger cube is equal to

Part B) The ratio of the total surface area of the smaller cube compared to the total surface area of the larger cube is equal to

Part C) The ratio of the volume of the smaller cube compared to the volume of the larger cube is equal to

Step-by-step explanation:

Part A) The perimeter of once face of the smaller cube compared to the perimeter of one face of the larger cube.

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

The scale factor is equal to the ratio of its corresponding sides

so

In this problem

The scale factor is equal to

therefore

The ratio of the perimeter of once face of the smaller cube compared to the perimeter of one face of the larger cube is equal to

Part B) The total surface area of the smaller cube compared to the total surface area of the larger cube

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

so

Part C) The volume of the smaller cube compared to the volume of the larger cube

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