Chapter 12.8, Problem 8PPS

To determine

Find whether the given pair of solids is similar , congruent , or neither.

Answer to Problem 8PPS

Congruent.

Explanation of Solution

Given:

  

Formula Used:

Two solids are similar if they have the same shape and the ratios of their corresponding linear measures are equal.

Two solids are congruent if they have the same shape and the ratios of their corresponding linear measures is 1:1.

Calculation:

The two solids are cylinders.

Find the height of the second cylinder by Pythagoras theorem :

  $=\sqrt{{17}^2-8^2}=\sqrt{289-64}=\sqrt{225}=15in.$

The ratio of the diameters of the cylinders is $\frac{8}{8}=\frac{1}{1}$ = 1:1

The ratio of the heights of the cylinders is $\frac{15}{15}=\frac{1}{1}$

=1:1

Since the ratios of the corresponding measures is 1:1 and both are cylinders , so the solids are congruent.

Since the ratio of the corresponding sides is not equal , the cylinders are not similar.

Hence,

The cylinders are congruent.