Chapter 12.8, Problem 10PPS

To determine

whether the given pair of solids is similar or not

Answer to Problem 10PPS

The given solids are not similar.

Explanation of Solution

Given:

  

Calculation:

In the first cylinder the diameter is 6 ft and the height is 2 ft.

In the second cylinder the diameter is 2 ft and the height is 6 ft.

The objective is to check whether the two figure are similar or not.

Two solid figures are similar if they have the same shape and their corresponding linear measurements are proportional.

In the given figure both are cylinder, so the solids are of same shape. Now check that whether the corresponding linear measurements are proportional or not.

Suppose the corresponding linear measurements are proportional, so

  $\begin{array}{l}\frac{6}{2}=\frac{2}{6}\\ 6\cdot 6=2\cdot 2[CrossMultiply]\\ 36=4\text{ False}\end{array}$

Since the result obtained is false, so the corresponding linear measurements of the given solids are not proportional.

Conclusion:

Therefore, the given solids are not similar.