The cylinders shown below are similar.
Two cylinders are shown side by side. The first cylinder has a height of 3 inches and a radius of 1 inch. The second cylinder has a height of 9 inches and a radius of 3 inches.
What is the ratio of their side lengths?
A. 1/27
B. 3/27
C. 1/9
D. 1/3
The ratio of their side lengths is the ratio of their heights, which is 3/9 or 1/3. Therefore, the answer is $\boxed{\textbf{(D) }1/3}.$
To find the ratio of the side lengths of the two similar cylinders, we need to compare their heights. The ratio of the heights of two similar objects is equal to the ratio of their corresponding side lengths.
In this case, the first cylinder has a height of 3 inches, and the second cylinder has a height of 9 inches. Therefore, the ratio of their heights is:
3 inches : 9 inches
Simplifying this ratio, we get:
1 inch : 3 inches
So, the ratio of their side lengths is 1/3.
Therefore, the correct answer is:
D. 1/3