Solution:

(i)Let the radii of two spheres be r₁ and r₂.

Given ratio of their radii = 3:7

Volume of sphere = (4/3)r³

Ratio of the volumes = (4/3)r₁³/(4/3)r₂³

= r₁³/ r₂³

= 3³/7³

= 27/343

Hence the ratio of their volumes is 27:343.

(ii)Surface area of a sphere = 4r²

Ratio of surface areas of the spheres = 4r₁²/4r₂²

= r₁²/r₂²

= 3²/7²

= 9/49

Hence the ratio of the surface areas is 9:49.

(b)Given ratio of volume of two spheres = 125/64

(4/3)r₁³/(4/3)r₂³ = 125/64

r₁³/ r₂³ = 125/64

Taking cube root on both sides

r₁/r₂ = 5/4

Ratio of surface areas of the spheres = 4r₁²/4r₂²

= r₁²/r₂²

= 5²/4²

= 25/16

Hence the ratio of the surface areas is 25:16.