Q. 16

# The surface areas

Answer :

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

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