Chapter 12.5, Problem 1CE

To determine

Tocheck:Whether the given solidsare similar or not.

Answer to Problem 1CE

No, the given solids are not similar.

Explanation of Solution

Given information:

The two shapes are shown below:

  

The bases of both shapes are similar as all circles are similar. The radius of first cylinder is $6$ and the radius of second cylinder is $3$ .

The ratio of radius of both the cylinders is:

  $\begin{array}{c}\frac{r_1}{r_2}=\frac{6}{3}\\ =2\end{array}$

The height of first cylinder is $12$ and the height of second cylinder is $8$ . So, the ratio of height of both the cylinders is:

  $\begin{array}{c}\frac{h_1}{h_2}=\frac{12}{8}\\ =\frac{3}{2}\\ =1.5\end{array}$

The proportion of the radius and heights of both the cylinders are not equal.

Therefore, the given solids are not similar.