Chapter 12.5, Problem 4CE

(a)

To determine

To find:The ratio of the areas of two spheres.

Answer to Problem 4CE

The ratio of the areas of two spheres is $4:9$ .

Explanation of Solution

Given information:The diameters of spheres are $24\text{cm}$ and $36\text{cm}$ .

Calculation:

Spheres are always similar and the scale factor of these spheres is equal to the ratio of the diameters. So, the scale factor of both spheres is:

  $24:36=2:3$

The ratio of the areas of the spheres is:

  $2^2:3^2=4:9$

Therefore, the ratio of the areas of both the spheres is $4:9$ .

(b)

To determine

To find:The ratio of the volumes of two spheres.

Answer to Problem 4CE

The ratio of the volumes of both the spheres is $8:27$ .

Explanation of Solution

Given information:Two spheres have diameters $24\text{cm}$ and $36\text{cm}$ .

Calculation:

Spheres are always similar and the scale factor of these spheres is equal to the ratio of the diameters. So, the scale factor of both spheres is:

  $24:36=2:3$

The ratio of the volumes of the spheres is:

  $2^3:3^3=8:27$

Therefore, the ratio of the volumes of both the spheres is $8:27$ .