Q. 305.0( 4 Votes )

# The volumes of two Spheres are in the ratio 64: 27. The ratio of their surface areas is

A. 9:16

B. 16:9

C. 3:4

D. 4:3

Answer :

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

Volume of the Sphere is: × π × r^{3} (where r is radius of sphere)

Surface area of the sphere is: 4 × π × r^{2} (where r is radius of sphere)

Let S_{1} and S_{2} be two different spheres.

(Volume of) S_{1}: (Volume of) S_{2} = 64:27

× π × (r_{1})^{3}: × π × (r_{2})^{3} = 64:27 (here r_{1} and r_{2} are the radii of S_{1} and S_{2} respectively)

(r_{1})^{3}: (r_{2})^{3} = 64:27

r_{1}: r_{2} = ∛64:∛27

r_{1}: r_{2} = 4:3

Now,

Let SA_{1} and SA_{2} be the surface areas of the spheres S_{1} and S_{2} respectively.

∴ SA_{1}:SA_{2} = 4 × π × (r_{1})^{2}:4 × π × (r_{2})^{2} (here r_{1} and r_{2} are the radii of S_{1} and S_{2} respectively)

⇒ SA_{1}:SA_{2} = (r_{1})^{2}: (r_{2})^{2}

⇒ SA_{1}:SA_{2} = (4)^{2}: (3)^{2}

⇒ SA_{1}:SA_{2} = 16:9

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

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