The surface areas of two sphere are in the ratio 16:9. The ratio of their volume is
Given: Surface area ratio of two Spheres is: 16:9
Volume of the Sphere is: 
× π × r3 (where r is radius of sphere)
Surface area of the sphere is: 4 × π × r2 (where r is radius of sphere)
Let S1 and S2 be two different spheres.
(Surface area of) S1: (Surface area of) S2 = 16:9
4 × π × (r1)2: 4 × π × (r2)2 = 16:9 (here r1 and r2 are the radii of S1 and S2 respectively)
(r1)2: (r2)2 = 16:9
r1: r2 = √16:√9
r1: r2 = 4:3
Now,
Let V1 and V2 be the volumes of the spheres S1 and S2 respectively.
∴ V1:V2 = 
× π × (r1)3:
× π × (r2)3 (here r1 and r2 are the radii of S1 and S2 respectively)
⇒ V1:V2 = (r1)3: (r2)3
⇒ V1:V2 = (4)3: (3)3
⇒ V1:V2 = 64:27
∴ The ratios of the volumes is: 64:27