Answer :

Given: Volume ratio of two Spheres is: 64:27


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.


(Volume of) S1: (Volume of) S2 = 64:27


× π × (r1)3: × π × (r2)3 = 64:27 (here r1 and r2 are the radii of S1 and S2 respectively)


(r1)3: (r2)3 = 64:27


r1: r2 = 64:27


r1: r2 = 4:3


Now,


Let SA1 and SA2 be the surface areas of the spheres S1 and S2 respectively.


SA1:SA2 = 4 × π × (r1)2:4 × π × (r2)2 (here r1 and r2 are the radii of S1 and S2 respectively)


SA1:SA2 = (r1)2: (r2)2


SA1:SA2 = (4)2: (3)2


SA1:SA2 = 16:9


The ratio of the Surface area of spheres is: 16:9

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