Chapter 12.5, Problem 3CE

(a)

To determine

To find:The ratio of the lateral areas of the prisms.

Answer to Problem 3CE

The ratio of the lateral areas of the prisms is $9:4$ .

Explanation of Solution

Given information:

The two right prisms are shown below:

  

Calculation:

Length of one of the side of the first prism is $9$ and the length of corresponding side of second prism is $6$ .So, the ratio of the sides of both the prisms is:

  $9:6=3:2$

Length of second side of the first prism is $12$ and the length of corresponding side of second prism is $8$ .So, the ratio of the sides of both the prisms is:

  $12:8=3:2$

Length of third side of the first prism is $12$ and the length of corresponding side of second prism is $8$ .So, the ratio of the sides of both the prisms is:

  $12:8=3:2$

The height of the first prism is $15$ and the height of second prism is $10$ .So, the ratio of the heights of both the prisms is:

  $15:10=3:2$

The scale factor of both the prisms is equal to $3:2$ .So, the ratio of the lateral areas of both the prisms is:

  $3^2:2^2=9:4$

Therefore, the ratio of the lateral areas of the prisms is $9:4$ .

(b)

To determine

To find:The ratio of the total areas of the prisms.

Answer to Problem 3CE

The ratio of the total areas of the prisms is $9:4$ .

Explanation of Solution

Given information:

The two right prisms are shown below:

  

Calculation:

As calculated in part (a), the scale factor of both the prisms is $3:2$ .So, the ratio of the total areas of both the prisms is:

  $3^2:2^2=9:4$

Therefore, the ratio of the total areas of the prisms is $9:4$ .

(c)

To determine

To find:The ratio of the volumes of the prisms.

Answer to Problem 3CE

The ratio of the volumes of the prisms is $27:8$ .

Explanation of Solution

Given information:

The two right prisms are shown below:

  

Calculation:

As calculated in part (a), the scale factor of both the prisms is $3:2$ . So, the ratio of the volumes of both the prisms is:

  $3^3:2^3=27:8$

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