If the surface areas of two spheres are in the ratio of 4 : 25, then the ratio of their volumes is

The ratio of the surface areas of two spheres is given as 4:25.

The formula for the surface area of a sphere is 4πr², where r is the radius of the sphere.

If the surface areas are in the ratio 4:25, then the ratio of their radii squared is also 4:25, because the 4π is a constant that would cancel out when forming the ratio.

Therefore, the ratio of their radii is the square root of the ratio of their surface areas, which is 2:5.

The formula for the volume of a sphere is 4/3πr³.

Therefore, the ratio of their volumes is the cube of the ratio of their radii, which is (2³):(5³) = 8:125.

So, the ratio of the volumes of the two spheres is 8:125.