Two similar cylinders have radii in the ratio six to seven. Circle the ratio of their surface areas. Is it six to seven, 36 to 49, 216 to 343, or 12 to 14?
There are two things we need to pay attention to here. The first one is that these are similar cylinders. And the second thing is that the radii are in the ratio six to seven. The formula for finding the surface area of a cylinder is two times 𝜋 times the radius squared times height. To find the surface area of a cylinder, we have to take the square of the radius. And that means the ratio of their surface areas will be the ratios of their radii squared, 36 to 49.
In this example, we were talking specifically about similar cylinders. But we can also say that, more generally, the ratio of lengths can be squared to find the ratio of areas, in similar figures.