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 surface areas?
A. 1/27
B. 3/27
C. 1/9
D. 1/3
1 answer
The formula for the surface area of a cylinder is $2\pi rh+2\pi r^2$, where $r$ is the radius and $h$ is the height. Since the two cylinders are similar, their corresponding dimensions have the same ratio. Therefore, the ratio of their surface areas is equal to the square of the ratio of their radii, or $\left(\frac{1}{3}\right)^2=\frac{1}{9}$. Answer $\boxed{\textbf{(C)}}$.
1 answer