Two similar cylinders have radii in a ratio of 2:5. What is the ratio of their volumes?

For similar solids, lengths scale by a factor $k$, areas by $k^2$, and volumes by $k^3$. The radii are in the ratio $2:5$, so the volumes are in the ratio $2^3:5^3=8:125$, choice C. Because the cylinders are similar, the heights are in the same ratio as the radii, which is why volume depends on the cube: radius squared times height. Choice A ($2:5$) is the ratio of the lengths themselves. Choice B ($4:25$) squares the ratio, which is the ratio of the areas. Choice D ($10:25$) multiplies the numerator by $5$ and does not follow any scaling rule.