Chapter 13.2, Problem 34SPR

To determine

To find: the ratio of the height of the small prism to the height of the larger prism.

Answer to Problem 34SPR

The ratio of the height of small prism to the height of larger prism is $8:9$ .

Explanation of Solution

Given:

Two similar prisms have the surface areas of $256\text{sq inches}$ and $324\text{sq inches}$ .

Concept used:

If the similarity ratio of two similar solids is $a:b$ , then:

The ratio of corresponding surface areas is:

  $a^2:b^2$ .

The ratio of corresponding volume is:

  $a^3:b^3$ .

This applied to all similar solid.

Calculation:

If two similar solids have a scale factor of  $a:b$ , then the surface areas have a ratio of is $a^2:b^2$ . The areas are in the ratio  $256:324$ .  The sides will be in the ratio:

  $\sqrt{256}:\sqrt{324}=16:18=8:9$ .

Hence, the ratio of the height of small prism to the height of larger prism is $8:9$ .