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 volumes?
A. 1/27
B. 3/27
C. 1/9
D. 1/3
The ratio of the volumes of two similar shapes is equal to the cube of the ratio of their corresponding lengths. In this case, the corresponding lengths are the radii and the heights. So, the ratio of volumes is:
$\left(\frac{3}{1}\right)^2\times\frac{9}{3} = 27$
Therefore, the ratio of their volumes is $\boxed{\textbf{(A) }1/27}$.