If the surface areas of two spheres are in the ratio 1 to 4, what is the ratio of their volumes?

Explanation

The surface area of a sphere is proportional to the square of its radius, while the volume is proportional to the cube of its radius. Given the surface area ratio is 1:4, the ratio of their radii is √1 : √4 = 1:2. Therefore, the volume ratio is 1³ : 2³ = 1:8.