Chapter 14.5, Problem 22WE

a.

To determine

To find the ratio of the surface area of the cubes.

Answer to Problem 22WE

The ratio of the surface areas is $4$ .

Explanation of Solution

Given information:

The given statement is:

“The diagram illustrates a dilation of three dimensional space. The dilation $D_{O,2}$ maps the smaller cube to the larger cube.”

  

Calculation:

The ratio of the area of the original image to its dilated image after dilation $D_{O,k}$ is $k^2$ times.

Hence, the ratio of the surface areas is $4$ .

b.

To determine

To find the ratio of the volumes of the cubes.

Answer to Problem 22WE

The ratio of the volumes is $8$ .

Explanation of Solution

Given information:

The given statement is:

“The diagram illustrates a dilation of three dimensional space. The dilation $D_{O,2}$ maps the smaller cube to the larger cube.”

  

Calculation:

The ratio of the volume of the original image to its dilated image after dilation $D_{O,k}$ is ${\left|k\right|}^3$ times.

Hence, the ratio of the volumes is $8$ .